MathDB
RMM2011, P 3, Day 1 - Determine the locus as line varies

Source: 0

February 25, 2011
geometrycircumcirclegeometric transformationtrigonometryconicsparabola

Problem Statement

A triangle ABCABC is inscribed in a circle ω\omega. A variable line ℓ\ell chosen parallel to BCBC meets segments ABAB, ACAC at points DD, EE respectively, and meets ω\omega at points KK, LL (where DD lies between KK and EE). Circle γ1\gamma_1 is tangent to the segments KDKD and BDBD and also tangent to ω\omega, while circle γ2\gamma_2 is tangent to the segments LELE and CECE and also tangent to ω\omega. Determine the locus, as ℓ\ell varies, of the meeting point of the common inner tangents to γ1\gamma_1 and γ2\gamma_2.
(Russia) Vasily Mokin and Fedor Ivlev
Back to ProblemsView on AoPS