CGMO 2012 (China Girls Math Olympiad 2012)- Problem 2


Circles Q_1 and Q_2 are tangent to each other externally at T. Points A and E are on Q_1, lines AB and DE are tangent to Q_2 at B and D, respectively, lines AE and BD meet at point P
Prove that

(1) \frac{AB}{AT}=\frac{ED}{ET};
(2) \angle ATP + \angle ETP = 180^{\circ}.
import graph; size(5.97cm); real lsf=0.5; pathpen=linewidth(0.7); pointpen=black; pen fp=fontsize(10); pointfontpen=fp; real ...

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About shivang1729

I am a young student who loves math . I like number theory and inequalities part the most , and preparing for Math Olympiads :)

Posted on Saturday,August 18, 2012, in Geometry, Problems and tagged , , . Bookmark the permalink. 2 Comments.

  1. I can’t solve it! Can you please give me a hint or the link where I can find CGMO 2012 solutions?

    Thanks

    Fdz

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