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parallel in a tangential trapezoid with 2 right angles

Source: Belarus TST 2009 2.3

June 13, 2020
geometrytrapezoidright angleparalleltangential quadrilateraltangential

Problem Statement

Given trapezoid ABCDABCD (AD∥BCAD\parallel BC) with AD⊥ABAD \perp AB and T=AC∩BDT=AC\cap BD. A circle centered at point OO is inscribed in the trapezoid and touches the side CDCD at point QQ. Let PP be the intersection point (different from QQ) of the side CDCD and the circle passing through T,QT,Q and OO. Prove that TP∥ADTP \parallel AD.
I. Voronovich
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