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Problem 7 of First round

Source: VI International Festival of Young Mathematicians Sozopol, Theme for 10-12 grade

January 13, 2020
geometryParallel Lines

Problem Statement

Let ABCDABCD be a trapezoid, where AD∥BCAD\parallel BC, BC<ADBC<AD, and AB∩DC=TAB\cap DC=T. A circle k1k_1 is inscribed in ΔBCT\Delta BCT and a circle k2k_2 is an excircle for ΔADT\Delta ADT which is tangent to ADAD (opposite to TT). Prove that the tangent line to k1k_1 through DD, different than DCDC, is parallel to the tangent line to k2k_2 through BB, different than BABA.
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