Problem 43: Balkan MO Shortlist 2003

Posts: 312
Joined: Mar 10, 2015

by henderson, Jul 29, 2016, 10:22 AM

$\color{red}\bf{Problem \ 43}$ Two circles $\Gamma_{1}$ and $\Gamma_2$ with radii $r_1$ and $r_2$ $(r_2>r_1),$ respectively are externally tangent. The straight line $t_1$ is tangent to the circles $\Gamma_1$ and $\Gamma_2$ at points $A$ and $D,$ respectively.The parallel line $t_2$ to the line $t_1$ is tangent to the circle $\Gamma_1$ and intersects $\Gamma_2$ at points $E$ and $F.$ The line $t_3$ through $D$ intersects the line $t_2$ and the circle $\Gamma_2$ at points $B$ and $C,$ respectively, diﬀerent from $E$ and $F.$ Prove that the circumcircle of triangle $ABC$ is tangent to the line $t_1.$
(Balkan MO Shortlist, 2003)

This post has been edited 4 times. Last edited by henderson, Sep 25, 2016, 2:51 PM

Math Path

Problem 43: Balkan MO Shortlist 2003

by henderson, Jul 29, 2016, 10:22 AM

0 Comments