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Concurrent

Source: Problem 11.3 - MOSP 2007, Chinese TST 2007 3rd quiz P1

June 19, 2007
geometryincentergeometric transformationhomothety

Problem Statement

Let ABC ABC be a triangle. Circle ω \omega­ passes through points B B and C. C. Circle ω1 \omega_{1} is tangent internally to ω \omega­ and also to sides AB AB and AC AC at T, P, T,\, P, and Q, Q, respectively. Let M M be midpoint of arc BC ( BC\, (containing T) T) of ­ω. \omega. Prove that lines PQ, BC, PQ,\,BC, and MT MT are concurrent.
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