MathDB
China 2010 quiz6 Problem 1

Source:

September 14, 2010
trigonometrygeometrycircumcircleincenterradical axispower of a pointgeometry unsolved

Problem Statement

Let ω\omega be a semicircle and ABAB its diameter. ω1\omega_1 and ω2\omega_2 are two different circles, both tangent to ω\omega and to ABAB, and ω1\omega_1 is also tangent to ω2\omega_2. Let P,QP,Q be the tangent points of ω1\omega_1 and ω2\omega_2 to ABAB respectively, and PP is between AA and QQ. Let CC be the tangent point of ω1\omega_1 and ω\omega. Find tan⁡∠ACQ\tan\angle ACQ.
Back to ProblemsView on AoPS