Most Wicked Geometry Problem | Math Olympiad Question

Comments · 158

• CR

  @cradleofrelaxation6473 · 1 year ago

  Math major here.<br>I’ve seen a lot of crazy solutions, this is definitely one of them!!

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• ST

  @stolenmonkey7477 · 1 year ago

  This problem was literally all of precalc in a single problem lmao

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• MO

  @MohamedShahid-q7e7o · 1 year ago

  I&apos;m from India . Your video is more useful to me.thanks

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• IL

  @ILoveCuty14 · 1 year ago

  I&apos;m Korean but I always watch your video when you upload video!

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• CL

  @cliffordbradford8910 · 1 year ago

  a lot of work to avoid tan15° as a real number.

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• PE

  @pedrojose392 · 1 year ago

  I am from Brasil. I have found a formula to this kind of problem: R1= 2*R*{[sin(w+u/2)/sin(u/2)-1]/[1/(sin(u/2))^2-1]}<br>For this particular case R=5, u=30 o &nbsp;and w=60 o <br>R1=2*5*[sin(75)/sin(15)-1]/[1/(sin(15)^2-1]<br>sin(75)/sin(15)=tg(75)=sqr(3)-2 and sin(15)=(sqr(6)-sqr(2))/4<br>R1=10*[sqr(3)+1]/[16/(8-4*sqr(3))-1]<br>R1=10*[sqr(3)+1]/[4/(2-sqr(3))-1]<br>R1=10*[raiz(3)+1]/[(2+sqr(3)/(2-sqr(3))]<br>R1=10*[sqr(3)+1]*[7-4sqr(3)]<br>R1=10*(7sqr(3)+7-12-4*sqr(3))=10*(3*sqr(3)-5) and that is it!<br>Now I am busy. Afterwards, i show how I found the formula.<br>That&apos;s all folks

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• MA

  @mahmoudhassan2541 · 1 year ago

  Iam egyptian and I do love your videos ❤

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• PO

  @Polonium.AMZ4 · 1 year ago

  wow ! what execelent question ! plesase give us more olympiad question

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• TX

  @txikitofandango · 1 year ago (edited)

  I tried this problem before watching the video. My steps:<br>Let r be the radius of the circle and let x be the distance from the center of the semicircle to the bottom point of tangency of the red circle. Then,<br>r² + (x+5)² = (r/(sin 15°))²<br>r² + x² = (5-r)²<br>forms a system of equations that can be solved... with Desmos :) Note that sin 15° = √(2-√3)/2 by the half-angle formula.<br><br>EDIT: I went back and did the algebra, it&apos;s not too bad if you substitute u = x + 2.5

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• MA

  @Maths_physics_lover · 1 year ago (edited)

  This lovely channel is for those who lack blood vessels as their body is dominated by maths concepts.<br>I AM ONE OF THEM THANKS FOR GIVING US THESE &nbsp;HOTS QUESTIONS

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• LA

  @lasalleman6792 · 1 year ago

  Took me awhile, but got 2.002 for r. &nbsp; &nbsp;Pretty close to suggested solution. &nbsp;Damn near had a brain freeze trying to figure it out.

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• AR

  @ArindamDutta-s4c · 1 year ago

  Geometry - 20%<br>Equation - 75%<br>SOO GOOOOOD!! - 5%

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