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tangential circles

Source: 2016 Korea Winter Program Test1 Day1 #1

January 27, 2016
geometrygeometry proposedtangent circles

Problem Statement

There is circle ω\omega and A,BA, B on it. Circle γ1\gamma_1 tangent to ω\omega on TT and ABAB on DD. Circle γ2\gamma_2 tangent to ω\omega on SS and ABAB on EE. (like the figure below) Let AB∩TS=CAB\cap TS=C.
Prove that CA=CBCA=CB iff CD=CECD=CE
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