Quadrilaterals 2 | CAT Preparation 2024 | Geometry | Quantitative Aptitude

Quadrilaterals by Ravi Prakash | Geometry Quantitative Aptitude for CAT 2024
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[@that_vet]

[SECOND LAST QUESTION] - sir I did this question by hit and trial method by applying the concept of Pythagoras triplets by observing 40 in my mind triplet (9, 40,41) just popped out and 41 being hypotenuse of triangle and side of rhombus. So answer is 4×41=164

[@gouravnagar2174]

Good

[@janhavibagal8141]

Thankyou so much sir for your amazing videos. We are so grateful for your amazing work.

[@sitharthr7838]

Quadrilateral is simply excellent💯

[@saurabhchand3516]

Hats off to u sir....Ur way of teaching is awesome.....ur video lectures r much better than offline coaching....Again thank u for making such nice videos🤘

[@Amansingh-uh1it]

Property of rombus is diagonals bisect each other at 90.

[@saurabhchand3516]

Yes Diagonals of rhombus bisect each other at 90 degree

[@suryavoroy3527]

Diagonal square sum of trapezium equals sum of square of non parallel sides plus 2 product of bases

[@ManuSrivastava_]

At 5:44 ∆AOB ~ ∆COD. please correct.

[@infotab9523]

thanks for CAT LEVEL

[@aadarshraghuvanshi126_c8]

Are all the concepts covered of geometry in this playlist !

[@PoojaSharma-yr3vu]

Very thankful!!

[@adityakeshri9377]

sir thank you so much for this kind of quality content , sir you don't know what this videos mean to us thanks a lot from all of us

[@-AbhishekSetia]

last question answer is 6.5 .... simply find side of rhombus by using formula which comes out 13 and r is half of side which is 6.5

[@friedsugar2701]

par sir ne 60/13, 4. something nikala hei

[@ManuSrivastava_]

Thank you so much sir.❤❤

[@17diamondlife]

the mid-point property, is it only for the isosceles trapezium or it can be applied to any trapezium?

[@tanmaydey3008]

Thank You Sir

[@Vineet84]

Sir can't we use the formula of area s minus a one and by that we will s euals to 20root 195 and then apply the formula a = r s by that we will get radius .But by that way my ans is coming out to be different

[@Shivam_General_Fitness]

Thanku sir

[@ayushkumar7497]

thanku sir

[@dishant_pawar]

Thank you sir for the this geometry set it really helped me alot, can you please answer that in last question r=median of right angle triangle so why cant be radius = 1/2(hypotenuse) i.e=13/2 ??

[@jaidevtyagi1033]

same doubt

[@bey0nder_beyond]

Sir i didn't get the concept of not taking square to find out max perimeter... 13:00

[@madhavbaheti9569]

Sir for finding that rhombus area Q we can also do it like this (total area of rectangle-area of 2 triangles =area of rhombus)

[@sayandeysarkar3354]

Yes even that is possible ans is same,but sir method is more lesser time to find out

[@AryanKhannaX]

Sir is the answer to the last question 60/13 instead of 6.5 on the basis of the assumption that this is not the largest possible circle inscribed within the rhombus because if it had been so, the circle would have touched all the sides of the rhombus and then the side of the rhombus would have been equal to the diameter of the circle.

[@user-gr3sy7tw9m]

Same doubt

[@harshitgoyal_30]

21:58 In the last question, can't we just draw a line parallel to AC by passing it from the centre. Hence, half of the side i.e. 13/2 = 6.5 will be the radius.

[@lihaz9911]

it looks like that because sir make a wide rhomus resemble square. Make it more narrower than it will break the illusion.

[@elcucuy2236]

In the last question how AC can be taken as the base if it is opposite to 90 degree angle?

[@shivamdrolia600]

Because for finding radius we have applied the concept that AC is a tangent to a circle at 90 degree so radius is perpendicular because of that 90 degree and we know, that we always consider base in which perpendicular is standing and conversely we have to calculate that perpendicular which is served as radius in the given question, if anyone find any mistakes in my comment, plz correct me pals.. Thanks

[@chhavimittal4862]

In the last second question, How can we assume that the figure is a rhombus. Is there any property by which we can prove that it is a rhombus?

[@Sonowalatwork]

Sir in the last question since triangle AOC is right angled Triangle, then 'r' will be the median..So is it we could have directly found out the Length of median since it's nothing but half of the hypotenuse..i.e. 13÷2=6.5

[@ashwindersingh678]

Hey simply get this by R = ab/c

[@ronitwankhede9411]

Exactly this is what I m saying but we are getting diff ans

[@shriharisriram2385]

Bro it's not median it just makes 90° , how did u assume it's the median?

[@Mamodo]

@@shriharisriram2385 I want to ask that is diameter of circle is equal to the side i.e. CB or AD

[@Dinesh__Jandagudem_29]

Instead we can consider AC equal to diameter of circle the radius is 6.5

[@abhishekbharti704]

22:24 For the last question how did we come to know that the point at which the diagonals of the rhombus are bisecting each other is the center of the inscribed circle, can anyone help me?

[@stalinparoyds472]

Yes, same issue with me here.

[@dmitrov6464]

*My Theory* 1. The nature of the question suggests that we should be considering the greatest Circle that can be formed inside the Rhombus. 2. If 1 is true then it is pretty evident that in order to obtain maximum diameter (hence radius), the diameter should align with the diagonals of the rhombus (aka the longest line segments in the figure). Hence the assumption.

[@kapilsarkar9223]

although there must be a rigorous proof of this somewhere out there , but we can safely assume this for the sake of symmetry . there are four identical triangles in there , why would the centre of circle choose one over other three . so the centre must be at the bisecting point . cheers.

[@vinaykapil1413]

use tangents theory, circle and rhombus sides

[@Dinesh__Jandagudem_29]

Yeah intersection of diagonals is the only point equidistant from all four sides

[@sanguine21]

Ya but in maximum area question of rhombus and square ,the question said all sides should be equal then why in rhombus one side is 40 and other is 41?

[@nithyasaitejareddysangati6311]

Hi Sir, How did you chose to draw the rhombus in the rectangle, The sum of adjacent angle points is not clear in the audio at 12:14.

[@mayankmehta183]

No sir THANKYOU!

[@gunjanagarwal2885]

In the last question, can't we take side of rhombus as the diameter of circle and then find the radius with the help of that??

[@-AbhishekSetia]

i was thinking the same

[@arnabbhanja5557]

No cause we don't know if the points of interaction of the circle and side will form a straight line or not

[@thechannel3420]

how height include 13 ?

[@bobbysgaming5570]

Sir why cant we use A=r*s in this

[@ankitkmr464]

No we cant because it is a concept of circle inscribed in a triangle but in this case circle is inscribed inside two triangles or a rhombus. So here, We can not use this concept.

[@rishabhgupta9033]

In last question, why the diameter of the circle not get equated to side if rhombus.

[@anshul5431]

Cuz it is a rhombus not a square. The side of a rhombus is slanted so it can't be equal to the diameter of the circle. If it had been a square then it will be so.

[@ziyadc8542]

we cant equate diameter to side of the rhombus because the diameter is not parallel to any of the sides.It is in this figure we feel that diameter is parallel to side.just google "circle inscribed in rhombus" and see the figure

[@SagarDwibedi028]

For maximum perimeter from a rectangle of area 2000 why can't we consider a square of side 20(sqroot(5)), it will lead to perimeter of 178.885 which is greater than 164.

[@alokkumargupta3121]

i dint get the last question. can any one explain? according to me r^2=12^2-(13/2)^2 ??? can any one explain?

[@arunadityarajjain1129]

You can't take length one side as 13/2, the circle is not touching AC at it's mid-point

[@bobbysgaming5570]

Then the ans will be totally different

[@Tara-vh4yk]

At 14 min how did we get -100x

[@mindfullmallu7511]

(a-b)².........☺️☺️☺️

[@saighodke6591]

i really like you

[@duddellaarunkumar3507]

In the last question when we get the side as 13 why cant radius be just 13/2=6.5 ?? Please reply

[@ankitkmr464]

Why divided by 2?

[@duddellaarunkumar3507]

@@ankitkmr464 consider the points on AD , BC of the rhombus where the circle touches the sides of rhombus , when we join the points where circle touches on AD,BC we get the diameter, which is also equal to side of the rhombus, as side is 13 , dia is 13 so radius is 6.5.

[@Coolcats19930]

My best guess. Not sure if it's correct... Please feel free to correct any inconsistencies When you join the points you are considering to be the diameter, the angle made on the points would still be 90 degree because there is a circle inside.. And the sides of the rhombus are acting as a tangent to the circle. So you get a quadrilateral with the adjacent angles 90 degree. This quadrilateral could be a trapezium as the the adjacent angles are now supplementary. It is not necessary that the opposite sides of the trapezium are equal... So it is possible that the length of the diameter is not equal to the sides of the rhombus

[@kanakh7775]

@@duddellaarunkumar3507 when we join those points, the line does not pass through the center and is not the diameter.

[@user-br9qv4iv2o]

@@kanakh7775 no the line do pass through the centre but we can't do side/2.Google circle in a rhombus and you'll know that diameter can't be equal to side just by seeing the figure.

[@hindavikadam3821]

How did we get A(🔺AOC)? The formula is 1/2* base* height right? But both OC and OA are not heights. Please help. I'm confused

[@chinmayeemohanty2311]

OA is hight for the ∆AOC right angled triangle ...

[@chaitanyatiwari6178]

Why can't we use appolonius theoram in the last question....I.e. sum of squares of diagonals = sum of squares of all four sides.... You said the same in your 16th geometry video sir.... Getting 26 sq. units the length of each sides by that formula....

[@shivanjalimore11]

even by that formula we are getting side 13

[@mindfullmallu7511]

I think this more expedite

[@bsvphotography7]

for the last question, it can be done this way too. 1/2 x d1 x d2 = base x height. 1/2 x 10 x 12 = 13 x h. h = 120/13 and so radius is half of height, i.e 60/13 :)

[@mindfullmallu7511]

D2=24.....good application!

[@hiteshpandey067]

how 13 can be taken as base in last part. the longest side should be hypotenuse.

[@kanakh7775]

Because we've made an altitude r which is falling on the base AC. What you're saying is correct, and we've already used that to find the area of traingle, this we're using to find the value of r.

[@hiteshpandey067]

@@kanakh7775 got it, thanks a lot.

[@BharathReddy98349]

@@kanakh7775 Why can't we simply use A=r*s?

[@kanakh7775]

@@BharathReddy98349 I forgot the question though, but wasn't r the altitude? And in the formula, A=r.s r is the inradius.. Shall I watch the video again to check the question?

[@ashwindersingh678]

@@BharathReddy98349 r is radius of circle inside the triangle not rhombus

[@navin1900]

Can anyone help me how centre of circle will be the intersection point of diagonal in the last question

[@itsme-lz6yh]

use geogebra site and make rhombus. u will get it

[@dmitrov6464]

[ LAST QUESTION ] My theory about why the center of the circle coincides with the intersection point of diagonals - 1. The nature of the question suggests that we should be considering the greatest Circle that can be formed inside the Rhombus. 2. If 1 is true then it is pretty evident that in order to obtain maximum diameter (hence radius), the diameter should align with the diagonals of the rhombus (aka the longest line segments in the figure). Hence the assumption.

[@Bella-sr4kl]

Thank You Sir ☺️