RMO 2000 Problem 1 - Trig Bashing in Geometry

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Let 𝐴𝐶 be a line segment in the plane and 𝐵 a point between 𝐴 and 𝐶. Construct isosceles triangles 𝑃𝐴𝐵 and 𝑄𝐵𝐶 on one side of the segment 𝐴𝐶 such that ∠𝐴𝑃𝐵=∠𝐵𝑄C=120∘ and an isosceles △𝑅𝐴𝐶 on the other side of 𝐴𝐶 such that ∠𝐴𝑅𝐶=120∘. Show that 𝑃𝑄𝑅 is an equilateral triangle.

Problem useful for I.S.I B.Stat B.Math Entrance, CMI Entrance and Math Olympiad
  1. Cheenta Academy for Olympiad & Research
  2. Indian Statistical Institute
  3. Chennai Mathematical Institute
  4. Math Olympiad
  5. RMO
  6. IMO
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Комментарии
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Nice problem. Reminds me of the days when we used to brainstorm such problems at 2 AM in night with Ashani Sir. Thanks to Cheenta Ganit Kendra and sir for introducing me to the love of Mathematics.

rudrtiwari
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Hello! Thank you so much... great way of explaining... could you please tell the software which you are using as a board? It would be great

krishiv
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<PBQ = 120°. Superb video 👍 and great explanation as usual. Would like my son to join PRMO program if you have? Can you please guide?

sonaraghavan