Circumcenter of a triangle | Special properties and parts of triangles | Geometry | Khan Academy

Multiple proofs showing that a point is on a perpendicular bisector of a segment if and only if it is equidistant from the endpoints. Using this to establish the circumcenter, circumradius, and circumcircle for a triangle
Watch the next lesson: www.khanacadem...
Missed the previous lesson?
www.khanacadem...
Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions. Wow. That's a lot. To summarize: it's difficult to imagine any area of math that is more widely used than geometry.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Geometry channel:
/ channel
Subscribe to Khan Academy: www.youtube.co...

[@khk2001]

Thank you for making such amazing videos😭 I have a geometry quiz tomorrow and this will definitely help

[@y10x85]

What score u got

[@ayushpatel8869]

Bruh this was 4 years ago

[@khk2001]

@@y10x85 LOL😭 ya, listen to what Ayush said. I don't remember what I got

[@javiertorres3372]

Welp I’m screwed tmr lol

[@PeeksAndGeeks]

@@khk2001 try harder

[@ScreamingMidget0]

wish khan academy was a real school.

[@khanacademy]

@GetMeThere1 Actually, this is a good topic for a video. You can have a triangle where the circumcenter is outside of the triangle.

[@kareslycorona7206]

yah when it is obtuse

[@vamparkolyptic]

wow 4 hours of suffering and i find this video i could've had no suffering if i had found this earlier. lesson learned. THANK YOU SO MUCHHHHHHHHH

[@lexinaut]

Great video! Considering the depth and beauty of the concept covered, I call it a Seriously Sublime Circumcenter. What is referred to here as RSH (right angle, side, hypotenuse) is also often called HL for hypotenuse leg. I'm not pulling anyone's hypotenuse leg here. It's helpful to know both abbreviations.

[@alllanguagessongs3283]

It is easy to understand .it is best vedio

[@Mythicaleldenlord]

Circumcircle

[@immortalmusic8213]

I think that postulate should be RHS instead of RSH

[@benjaminteitelbaum1073]

Is the radius of a circumscribed circle about an equilateral triangle, always double the radius of that triangle’s inscribed circle? If so, please show proof ONLY using geometry, not trigonometry, or Pythagorean theorem, but just postulates. Please do a video about this. Is the equilateral triangle with circumscribed and inscribed circle a special case, or is this true for all triangles hat have both inscribed and circumscribed circles? Thank you!

[@elithebeef3445]

Thanks sir ! You helped me with my homework !!!!

[@AlRoderick]

@GetMeThere1 Think of it like this. The perpendicular bisectors are lines, so they go on forever in both directions. If the triangle has two small angles and one big one, say 10 degrees, 20 degrees and 150 degrees, the lines wouldn't intersect until well outside the triangle, because the lines continue on forever outside the triangle. The circumcenter would be past the side opposite the big angle. The important bit is that all the points of the triangle are on the circle edge, not inside it.

[@Kurtlane]

Great! But how to find the center of a circle incide a triangle, which touches triangle's edges? Would it always be the same center as the circumcenter in this video? If not, when would they be the same? Thanks.

[@davidbrisbane7206]

It was not proven in this video that the vertical bisectors of the three sides of the triangle actually intersect. However, to show that the distance between the circumcenter and the three vertices are the same distance, it is only necessary to construct two vertical bisectors and they just use the proof in the first part of the video to show they must be the same even with only two intersection bisectors.

[@GetMeThere1]

I've never heard of this before. Cool! But it prompts me to ask: does ANY triangle drawn in a circle have its circumcenter at the center of the circle? And, of course, the answer is obviously: "No." I can draw a triangle in a circle whose area doesn't even COVER the center of the circle. ....which then makes me ask: Do all possible triangles drawn in a circle that DO cover the center of the circle share their circumcenters? Again, no, because I can imagine a triangle that wouldn't work...

[@Three60DrSports]

RSH and RHS are both stating the same thing. It’s just stating that the two triangles have a Right Angle (which are congruent) a Hypotenuse that is congruent and another Side that are congruent. Another name you may see in textbooks or from your teachers which states the exact same thing is HL, which stands for Hypotenuse Leg. HL assumes you already know you have a right triangle. So as long as their hypotenuses are congruent and at least 1 more side (Leg) is congruent, then you know the two triangles are congruent by HL.

[@GetMeThere1]

@AlRoderick : Good point. So yes, the circumcenter could be far outside the triangle--and it would represent a HUGE circle (as big as you please, actually). So...circumcenters can easily be outside their area....I infer that all triangles with all apexes on a circle ALL share the same circumcenter, and, of course, it's at the center of the circle. Thanks! Pretty interesting and counter-intuitive (for me). Perhaps this points toward the connection between pi and trigonometry and triangles.

[@amirulislamsiham7953]

Thank you so much brother

[@GetMeThere1]

@khanacademy : Ah! OK, cool. I'd like to hear more...

[@lilpandaboyy]

wow... i just started circumcenter of a triangle in class... :)

[@NHASAN-jw7yc]

Sir awsome explanation💞🔥

[@SamuelKioEDH]

in fact, just thinking about it should clearly prompt you to see this.

[@SamuelKioEDH]

actually the answer is obviously 'yes'. as khanacademy said, triangles can have a circumcenter outside of a triangle. In fact, ANY obtuse triangle has a circumcenter outside of the triangle.

[@999huzar]

oh! amazing khan.i like it.than you khan.

[@ramlalravindra1289]

I always forget these special points is there mnemonic or something else to not get confused.

[@Bummersx7]

Thank you

[@klusadus2]

Oh and by the way, thanks for the new vid, keep em' coming!

[@XLCreepers]

Why can't you be my teacher.

[@khk2001]

XLCreepers that'd be wonderful

[@klusadus2]

FIRST! I love you Khan!

[@mahuyaganguly5623]

Does this only happen for an isosceles triangle?

[@digitalconsciousness]

As far as the circumcenter goes, it applies to all triangles. If you would like to try it on paper, draw a few circles, then draw different triangles in each one to experiment. The points of course have to exist on the circle. Then draw the perpendicular lines in from the sides and they will always meet up at a single point - the circumcenter.

[@johncunningham7311]

love this ish

[@amanrubey]

beautiful

[@maxaschers]

circumcision

[@Alex-ds9on]

Hi Mrs Johnston

[@OneBitGaming]

This video allows me to be absent from school.

[@mevatunc6732]

I come here after school, why am I even going to school???

[@SbLox]

same

[@chinmayg3108]

👍👍👍

[@edwinrajoo6874]

can the circumcentre be outside the triangle?

[@nickpocchia3445]

Rickey Zee yes in an obtuse triangle

[@kumarsaurav8885]

Isn't it RHS?

[@zakisensei]

Um whaaat?

[@maithaalsaeedi8234]

00100 math :))

[@carissapalamar63]

hi

[@Lex-iy9kv]

I hate geometry so much. I took pages of notes and I still don't understand anything!

[@likhithsugganahalli]

is a centroid and a circumcentre the same point

[@kushtrimsertolli]

No

[@logitht9075]

I hurt maths

[@IsabellaLove97]

i hate geometry :/