How do you find the radius given a chord and a perpendicular bisector?

[@ffyfy1]

ffyfy1 I’m just a carpenter.... But through the years not knowing much algebra or trigonometry. I have always used this simple formula when building. To find the radius when the cord and the height are known. Try this. R=(Width squared) divided by (height times 8) Plus 1/2 Height. Very simple and never fails. Of course now I just pull out my construction master calculator.

[@MrHelpfulNotHurtful]

Thanks!! 😊

[@jimgnandt5190]

That works great. I'm an electrician and I can use that for segment bending to find an unknown radius of a curved wall.

[@ffyfy1]

I have kept a journal of these layman’s solutions through the years. I hope you get a chance to use this one Sparky.

[@illaraghavendiran8315]

Amazing video man! I have a math test tomorrow and I wanted to do some final review, and you couldn’t have summed everything up better. You are so underrated, but so helpful. Thank you!

[@MrHelpfulNotHurtful]

I really appreciate your feedback! I keep hoping more people will find the channel. I’ll just keep making videos until they do. 😎

[@jessiewang7254]

Thank you so much. I hope this channel grows, it's really helpful.

[@MrHelpfulNotHurtful]

Yay! Thanks. 😎

[@ottiokambozani3725]

It helped me a lot because I was taught about it in grade 11 but now this year I have forgotten about it🙌🏿thanks a lot Mr

[@MrHelpfulNotHurtful]

I’ve got your back! 😎

[@zncvmxbv4027]

Just measure the chord with a tape. Then find the center and measure from center to the circle. Then do r-half of the chord squared plus half the chord squared equals r squared and math it out on the site. Personally I’d set up a formula in excel or google sheets and just have to enter both the chord length and the distance from the circle to the center of the chord and then boom. You look like a boss!

[@MrHelpfulNotHurtful]

Thanks! 😊

[@maheshjangid732]

This is simple idea make half chord length and squaredo and height do square both counting add then divide by height multiple 2 then results perfect radius

[@Grudairian]

Just want to say thanks! I was trying to find the radius of a sphere when I had the diameter and height of a cap, this approach worked fantastic for me.

[@MrHelpfulNotHurtful]

Yay! I’m so glad I could help. I appreciate your feedback. 😊

[@RFUN109]

Thanks so much for this video, I am in 10th grade and this really helped me understand my homework assignment.

[@MrHelpfulNotHurtful]

You are very welcome. I got your back!

[@bgdavenport]

I CARE! This is particularly useful for paper modeling which relies heavily on truncated cones. If I which to cap the cone with circular sections, it helps to know the radii! I knew this formula decades ago and was on the verge of solving it when it occurred to me that I should check first before reinventing the wheel. Thank you. BTW, I simplified (and checked) the formula: r= x2 + y2 / 2y That is of course, x squared + y squared = twice y.

[@MrHelpfulNotHurtful]

bgdavenport Ok. That makes a lot of sense. Thanks for the feedback! 👍

[@jupiternextmusic8764]

I thought you could use the law of intersecting chords theorem, which says AM * BM = PM * MX, where X is the point on bottom continuing the bisector all the way down. Therefore 5 * 5 = 25, so the length of PX would be 25 / 3 = 8.3, then 8.3 + 3 = 11.3 for a diameter of 11.3. Divide by 2 and you get the radius = 11.3/2 = 5.65. R = 5.65 I guess there are multiple ways to solve? :) Thanks!

[@MrHelpfulNotHurtful]

You are right. That works too. 😊

[@andydaniels6363]

This was my thought, too: this gives you a direct computation instead of having to set up and solve a quadratic equation. You should take more care with your round-off errors, though. Your final result is not a very good approximation to 17/3.

[@UCLAursinho]

Thanks for the video but I suggest using the intersecting chords theorem where the second chord is the diameter (d) passing through P, M and O to the other side of the circle ( lets call it Q) The theorem basically says that the lengths of the chord segments for both chords on each side of the intersecting point when multiplied together are equal. So in your example: AM × MB = PM × MQ 5 ×5 = 3 × (d-3) 25=3d-9 34=3d 34/3=d=2r r=34/6=17/3 Same answer but less constuction and simpler algebra.

[@MrHelpfulNotHurtful]

That did not occur to me. That you so much. I’ll do it that way next time. 😎

[@phenphea5809]

Simple way I always use What do you think? 5ChordA×5ChordB=25 25÷3(Bisector of chord AB)=8.3333333333 8.3333333333+3(Bisector of chord AB)=11.3333333333 Radius of circle O (R=11.3333333333÷2=5.6666666667)

[@MrHelpfulNotHurtful]

That works great! Thank you for sharing. 🙏

[@Rabbaduck]

A straight edge and square p downwards then join a straight line from p to b. Get the halfway point of p to b then square that down. Where those two squared lines intersect is your radius... hope that helps. I didnt read all the comments so I'm not sure if someone posted this.

[@MrHelpfulNotHurtful]

Ronnie Sanchez Thank you so much. This is very helpful! 😊

[@mirandagarner8198]

You're the goat man

[@MrHelpfulNotHurtful]

Yay! Thanks :-)

[@devashishsingh5077]

Had to use this in real life.. Did a google search to get here.. Thanks..

[@MrHelpfulNotHurtful]

Awesome! You are very welcome. 😊

[@ghjtredsw]

My chord is 4. What is the length of the bisector?

[@MrHelpfulNotHurtful]

That is not enough information. In my video, we are given the length of the chord and the bisector and we are asked to find the radius. If you are trying to find the length of the bisector, we need the length of the chord and the radius.

[@benwatson2918]

Good algebra. It is very easy to find the radius using compass and ruler. bisect any 2 chords to find the center of the circle.

[@MrHelpfulNotHurtful]

Ben Watson Thanks 😊

[@thekatybabes6172]

omg i finally understand THANK YOU SO MUCH!!!!

[@MrHelpfulNotHurtful]

Yay! You are super welcome! 😎

[@championn3c574]

Thanks for that, I got a bit lost when you pulled that 9 out of the hat but it's 35+ years since my last algebra lesson.

[@MrHelpfulNotHurtful]

You are very welcome. Sorry about the rando 9.

[@yeyekwang5316]

Thank You ! I solved my problem .

[@MrHelpfulNotHurtful]

Ye Ye Kwang You are super welcome. 😊

[@Mahdi-wp5vs]

Thanks, but if i given chord length and Arc length , can you find the radius

[@MrHelpfulNotHurtful]

Sadly, I do not know how to solve this. I think it is beyond the scope of high school geometry.

[@UCLAursinho]

I think you need to know another piece of info to solve such as the interior angle.

[@stevenmathews7621]

Make gates, when there's curve on the top of the gates, need to give the steel bending joint the radius Simplified for quick use at work... If AB/2 = x, and perp bisector = y, then r = (x² + y²) / 2y

[@MrHelpfulNotHurtful]

Wow Thanks!!

[@malaikabaig4929]

tysm!!

[@MrHelpfulNotHurtful]

You are very welcome. :-)

[@musicmikeish]

It can be solved with trigonometry too though it's a bit lengthy: I generated a formula: Radius = (½chord ) / Cos { 90 - (2tan_invs(bisector÷0.5chord)) } R= (0.5*10) / Cos { 90 - (2tan_invs 3÷(0.5*10) } R= 5.67

[@MrHelpfulNotHurtful]

Thank you! Amazing. 🤩

[@Carp1n_ter0]

Yes it can also with a tape measure and a string/chalk line

[@ajitt7939]

Thank you! You can get it also by (PM^(2)+BM^(2))÷(2×PM)

[@MrHelpfulNotHurtful]

You are correct. I appreciate your contribution! 😊

[@blopbop5405]

Thank you very much. I just used this information for a real life scenario. I'm designing a desk with a curve for the L-shape. I want the curve as tight as possible so I can swivel more and roll less but I also want the curve wide enough that I can roll up to the desk and be within 4" of my keyboard. So for me, the chord was the width of my office chair 25" and the length of the perpendicular bisector was 4". After doing the math, the radius of the circle for my corner desk will need to be 21.53 inches.

[@MrHelpfulNotHurtful]

That’s awesome! Thank you for sharing. I’m going to use this as an example with my students! 😎

[@bellekiprop9650]

I had the same problem with designing the top arc of a metal bed. Thanks to this guy

[@jh5866]

Great stuff, you da man

[@MrHelpfulNotHurtful]

Thanks! I appreciate the feedback. 😊

[@Afitkid]

Thank you so much I understand this topic more!

[@MrHelpfulNotHurtful]

Yay! I’m so glad I could help. 😊

[@ericksonjoseph2532]

lets push this to one million views guys

[@chowder2275]

Thank you so much 😊

[@MrHelpfulNotHurtful]

You are quite welcome. 😊

[@JorgeLuis-ls6bx]

Amaizing truly amaizing..thank you so mucho

[@MrHelpfulNotHurtful]

Yay! You are super welcome. :-)

[@davehubbard4285]

in construction more often use AxA +PxP find square root +2xP = radius

[@MrHelpfulNotHurtful]

Thanks!

[@leonelantonio2779]

A circle has a radius of 15 cm, how far from the center is a chord of 24cm length? A chord is 10 cm from the center. How long is it?

[@MrHelpfulNotHurtful]

For your first question, draw a segment from the center to the end of the chord. This is a radius which is 15. Draw a segment from the center to the chord. This is what you are looking for so label it x. Half of the chord is length 12. The x and the 15 and the 12 form a right triangle with hypotenuse 15. Use the Pythagorean Theorem to solve for x. a squared plus b squared equals c squared.

[@MrHelpfulNotHurtful]

For the second question you will form the same triangle and use the Pythagorean Theorem again. This time the x will be one side of the chord. The other two sides of the triangle are 10 and 15 (the radius is again the hypotenuse). Once you find x, you have to double it to get the length of the whole chord.

[@TangodownNZ]

So if I got 6760/12 and reduced that down to 1690/3 (by dividing both by 4) Does that make my radius 563?

[@MrHelpfulNotHurtful]

Yes. Rounded to the nearest whole number. 😎

[@TangodownNZ]

Thank you this helped me to copy my bbq plate

[@TangodownNZ]

It is better to solve it this way rather than with a compass and straight edge anyway. Thank you

[@MrHelpfulNotHurtful]

I really appreciate your feedback. 😊

[@bernielittmann5098]

The formula used in Traffic Collision Reconstruction for calculating the tire impression in a Yaw ( no braking and hard skid to the left or right ) C= Chord & M=Middle Ordinate. ((C x C) / 8 X M) + (M / 2). This will give you the same outcome.

[@MrHelpfulNotHurtful]

Thanks!

[@ritawashere5787]

Hi Bernie, I'm not a student learning algebra, I'm a grandma thats raising her 4 yr. old grandson, trying to build a large "Hamster wheel" but large enough for a cat. I have my base with my wheels attached. Now the problem is trying to find out the size of the wheel I need that will be rolling on the base. It's been a number of years since I have been out of school. And even then I was no mathematician. But that doesn't mean I haven't enjoyed taking this trip down memory lane. You mentioned in your comment that you are able to get the same result with your sentence. So Bernie these might seem like silly questions, dare I say stupid, but here I go. Is the number 8 in your sentence always an 8 and always there? Also the same goes for the number 2 that's in the sentence? My measurements are C= 5 5/16" Perpendicular bisector= 2" I think with the measurements I've got I could at least have the arc and then maybe from there be able to figure out the size of the wheel. I apologize for being wordy, it goes with the territory, I'm 52 yrs. Old. I hope this comment finds you well, have a great day. ☺️

[@fmcguire51]

thanks ... exactly what i’ve been looking for ... i need to calculate how best to lay a carpet in a large room shaped like a partial segment :)

[@MrHelpfulNotHurtful]

Yay! Real world applications!

[@fmcguire51]

I can explain how this might be calculated with compass and straightedge or folded paper when knowing only the chord length and length of chord to circumference: 1) draw a unit circle (radius of 1 unit of any measurement system) and draw a line through the center, edge to edge (diameter line) and another line perpendicular to the diameter line you just drew 2) cut a rectangular piece of paper (a bit larger than the diameter of the circle) in the ratio of the chord to the perpendicular (chord to circumference measurement) to form a rectangle 3) fold the rectangular piece corner to corner to form a rectangle and cut along the fold 4) slide the triangular paper keeping its base parallel to the diameter line and the angle tip of the triangle on the circumference until the hypotenuse edge of the triangle touches the circumference exactly where the diameter perpendicular line touches the circumference 5) mark the base of the triangle where it touches the circumference (opposite the angle tip) and draw a chord along the base of the triangle and lines from the chord’s end points to the center of the circle 6) last, measure the resulting chord and apply the scale of chord measurement to unit measurement

[@MrHelpfulNotHurtful]

Thanks! That's been bugging me for 2.5 years! :-)

[@bengrant4724]

@@MrHelpfulNotHurtful Another real world application is determining the radius of a curved monitor to find the best viewing distance for the whole screen. Your explanation was excellent!

[@MrHelpfulNotHurtful]

@@bengrant4724 Thank you! I can see the application now. I will definitely share that with my students. :-)

[@thekatybabes6172]

what if the chord is only one number and not split up into two?

[@MrHelpfulNotHurtful]

If there is a segment that is perpendicular to the chord, it will always be at the midpoint. So take the one number they gave you and split it in half yourself. 😊

[@thekatybabes6172]

@@MrHelpfulNotHurtful thanks!

[@TheDefeatest]

Thanks for the vid, but why dont you solve the r value at the end, or what I mean by that is divide 17 by 3 to get your final number?

[@MrHelpfulNotHurtful]

17/3 is exact and cannot be reduced further. If you divide you get 5.6666666... which you you must round to 5.67 or 5.7, but this is an approximation. Students are welcome to put a decimal as long as your teacher allows it. I prefer the fraction because it is exact.

[@AuldViolin]

If you round up to .6875 you could look up from your clip board and tell the builder dude ‘set your trammels to 8-11/16 bro’

[@joshuamillan7610]

Yes you can solve for the radius only using a compass and straight edge

[@joshuamillan7610]

If given the rise above chord

[@MrHelpfulNotHurtful]

You rock

[@jaynabellerioflorido8074]

In a circle,a chord with length 10 units is 2 square root of 6 units away from its center.find its radius.Can you help me in this question?

[@MrHelpfulNotHurtful]

So sorry. I am too busy at work these days to solve new problems. 😔

[@dilmuradtab2846]

Thanks 🙏

[@MrHelpfulNotHurtful]

Dilmurad Tabaldyev Anytime! 😎

[@Fost32]

Very helpful!

[@MrHelpfulNotHurtful]

Yay!

[@luyandatsabedze3490]

Thank youuuu😭❤️

[@MrHelpfulNotHurtful]

You are very much welcome. 😊

[@samanthanicoleevangelista1994]

may I ask how can I get the length of the bisector of the chord??

[@MrHelpfulNotHurtful]

In my example, the bisector was given. In the example you are talking about, what all is given? Are you given the chord length and the radius for example?

[@Chloe-o1h]

life saver!!!

[@MrHelpfulNotHurtful]

Yay!! 😄

[@jayster9404]

thank you :)

[@MrHelpfulNotHurtful]

You are very welcome. :-)

[@xbiggrape8802]

What if 3 was x? How would you solve?

[@xbiggrape8802]

Or R in this case

[@MrHelpfulNotHurtful]

Unless they give you some additional information (like the radius) that would not be enough information.

[@JonnovanderRiet]

Thanks for this

[@MrHelpfulNotHurtful]

You are super welcome!

[@iamjayu]

Thank you 😊

[@MrHelpfulNotHurtful]

You are very welcome. 😊

[@ary3397]

thanks for the help!

[@MrHelpfulNotHurtful]

You are super welcome. :-)

[@ireto6223]

What is the area bounded between OP and r?

[@MrHelpfulNotHurtful]

ire to Do you mean the area bounded by OP, OB and the intercepted arc?

[@ireto6223]

@@MrHelpfulNotHurtful exactly.

[@MrHelpfulNotHurtful]

@@ireto6223 Here's how you find the sector area: kzbin.info/www/bejne/mICzp52JlK6bpK8

[@ireto6223]

@@MrHelpfulNotHurtful Thank you so much. That helps a lot.

[@alirezafarshad4169]

it was helpful , thanks alot :)

[@MrHelpfulNotHurtful]

alireza farshad Glad I could help. 😎

[@aryanbawal129]

I have one chord length and radius I need to find the measurements of the whole chord

[@MrHelpfulNotHurtful]

Aryan Bawal I don’t follow your question. You say you have one chord length. Then you say you need to find the whole chord. What do you mean? Can you rephrase the question?

[@aryanbawal129]

MrHelpfulNotHurtful it’s a diagram with a chord than a line going through the middle intersecting the chord then near the left there is a right triangle, bottom of the triangle near the radius is 13mm then top right from the line there is 8mm the question is what is the length of EF, EF is the chord.

[@MrHelpfulNotHurtful]

Aryan Bawal Are you saying that the radius is 13 and that is the hypotenuse of the right triangle? And one leg of the right triangle is 8? And the other leg is half of the chord? If so then you can find the missing side of the right triangle using the Pythagorean Theorem. X^2 + 8^2 = 13^2. So x^2 + 64 = 169. So x^2 = 105. So x = radical 105 which is about 10.2. This is half the chord, so you double it. The chord is about 20.4. If I am still not imagining the correct diagram, I will need you to send me a link to a picture.

[@truesolution6069]

How did you know the center point?

[@MrHelpfulNotHurtful]

I'm not sure what you mean when you say "know the center point." We know that is exists because all circles have a center point. We are allowed to simply draw a dot inside the circle to represent the center.

[@truesolution6069]

The centre point is Radius r minus the given quantity. r-q, my question is, do you know any other way to find center point from the example you have given.

[@MrHelpfulNotHurtful]

@@truesolution6069 This is the only method that occurs to me.

[@ikemuoma8495]

Brilliant!!!

[@MrHelpfulNotHurtful]

ike muoma Yay! 😊

[@RajRaj-yp5kx]

Phenomenal.

[@MrHelpfulNotHurtful]

Raj Raj 😊

[@SalyZaki-ht1mu]

what the meaning of the orthogonal chords?

[@SalyZaki-ht1mu]

please any one answer as fast as he can .

[@MrHelpfulNotHurtful]

Orthagonal means perpendicular. Orthagonal chords are perpendicular chords (two segments stretching from one side of the circle to the other that are perpendicular to each other).

[@SalyZaki-ht1mu]

ok thanx bro

[@atulchauhan5565]

Why did you elongated the equation. Idk

[@MrHelpfulNotHurtful]

Thanks for the feedback. I'll try to be more concise in the future.

[@ollopa1]

(x^2 + h^2)/2h => (5^2 + 3^2)/6 = 34 / 6

[@MrHelpfulNotHurtful]

ollopa1 Thanks 😊

[@mawillies_01]

Thanks a lot ❤ I man

[@MrHelpfulNotHurtful]

You are super welcome! 💙😊

[@blurse1652]

THANK YOU

[@MrHelpfulNotHurtful]

You are very very welcome. :-)

[@willvincentparrone3339]

The hidden joke though XDDD *Credits to ester

[@ramit_m]

Yes you can solve it with a scale and tools

[@MrHelpfulNotHurtful]

Thanks. Post a link if you know any videos of this.

[@JaiChavan]

Thanks.

[@MrHelpfulNotHurtful]

You are very welcome.

[@Droningonuk]

Yes you can solve this with just a compass

[@MrHelpfulNotHurtful]

Tell me more.

[@Droningonuk]

@@MrHelpfulNotHurtful sorry you would need a ruler too*

[@coryholmes1232]

🙌

[@MrHelpfulNotHurtful]

Yay. 😊

[@charlesmunyoro633]

wow, thank man

[@MrHelpfulNotHurtful]

You are super welcome, my friend.

[@johnx9318]

It would have helped if you had bothered to work out line three. Some of us don't know what you did to get these numbers. And that is very frustrating.

[@MrHelpfulNotHurtful]

If you are taking about the numbers that are present in the problem when the video begins, they are given information. I did not write this problem, someone asked me to solve it so I tried to help out as best I could.

[@johnx9318]

@@MrHelpfulNotHurtful No, it was the third algebraic line. I had no idea how you arrived at the numbers you did. All good up till then, but crashed.

[@MrHelpfulNotHurtful]

@@johnx9318 I see. You don’t understand how to multiply (r-3)(r-3). Sorry I didn’t go into detail about it. It was an algebra 1 concept so I made the false assumption that everyone already knew that part. I’ll try to be more thorough in the future.

[@johnx9318]

@@MrHelpfulNotHurtful Thanks - I try very hard to understand and learn maths, but there are always log-jams. This one was going very well until I crashed.

[@anthonypeterson5618]

Without a calculator is better than SOHCAHTOA

[@MrHelpfulNotHurtful]

Old school. I like it.

[@shielasabbang8420]

I did this, but my teacher said i'm wrong.

[@MrHelpfulNotHurtful]

Oh no. Did your teacher explain some other way? I really believe my method is sound.

[@shielasabbang8420]

She actually didn't explain. She just gave it as assignment then the next day she collected it without speaking anything about it. We wanted to ask but she's terrifying. She actually teaches well but she, well she's just unapproachable.

[@geoffarone9938]

LmAo AmesTaccciaao

[@MrHelpfulNotHurtful]

Geoff Arone 😬

[@thekingoflife124]

Talk in hindi pagal

[@MrHelpfulNotHurtful]

I don’t know how. 🤷🏾

[@mikemoreby1512]

Who cares ?........

[@dsingh2391]

Math is the only reason I want school over with

[@MrHelpfulNotHurtful]

DSingh23 My daughters feel the same way! 😬

[@sonidevi9953]

Thank you so much ❤

[@MrHelpfulNotHurtful]

You are very welcome. 😊

[@danfall8233]

I was looking for some convoluted formula for a chord (for a woodwork project) and dude just pulls out Pythagoras... I'm an idiot lol! Cheers man, great video

[@MrHelpfulNotHurtful]

Glad to help! 😎

[@Xyz-sd7ub]

R = 5.67 units

[@MrHelpfulNotHurtful]

Thanks 🙏

[@lukedarr1617]

Ok so I just had this problem but it was a real world application instead of for one of my classes this time. I needed to cut a curve out of some plywood and I only knew the width (P to M in the video) of the sector and the hight of it ( A to B in the video). I did some testing and this is how it can be done. 1. Measure inside angle from B to P. Let's say it was 15° in the video. 2. Draw a center line through P and M and make it continue past M a good bit. 3. Take angle_(BP) multiply it by 2. (We would get 30°). 4. With your protractor laying flat on the line you made in step 2, slide it along the line until the protractor crosses the circumference at 30°. 5. The center point of the protractor will be the center of the circle. Plot that point then all you have to do is measure the radius from that point to the outside of the circle segment. (Edit) in step 4 when you do this with large circles(or skinny segments) it helps to lay a ruler or straight edge across the protractor at the angle you found in step 3 so that it will still cross the circle.

[@MrHelpfulNotHurtful]

Luke Darr Thank you so much!! I really appreciate the practical application. 😎

[@saffymillar5207]

very helpful. taight more than math teacher did Tysm

[@MrHelpfulNotHurtful]

You are very welcome!

[@pluto_kun]

Thanks that was pretty helpful!

[@MrHelpfulNotHurtful]

So glad I could help. 😊

[@juantapia9648]

Intersecting cords theorem?

[@MrHelpfulNotHurtful]

Juan Tapia Never heard of it. Is that what this involves?

[@fheyirduh8197]

thank you!!!!!!!!!!!!!

[@MrHelpfulNotHurtful]

You are very welcome :-)

[@almond1117]

thanks i appreciate you

[@MrHelpfulNotHurtful]

Aww. It feels good to be appreciated!!

[@almond1117]

MrHelpfulNotHurtful yeah it does, my teacher barely teaches so I always go to KZbin for help

[@MrHelpfulNotHurtful]

Browse the home page of my channel: kzbin.info Hopefully you will find helpful videos for years to come. :-)

[@almond1117]

MrHelpfulNotHurtful will do