MathDB
Iran(3rd round)2009

Source: Problem 3 Geometry

September 13, 2009
geometrytrapezoidcircumcirclegeometry unsolved

Problem Statement

3-There is given a trapezoid ABCD ABCD in the plane with BC∥AD BC\parallel{}AD.We know that the angle bisectors of the angles of the trapezoid are concurrent at O O.Let T T be the intersection of the diagonals AC,BD AC,BD.Let Q Q be on CD CD such that \angle OQD \equal{} 90^\circ.Prove that if the circumcircle of the triangle OTQ OTQ intersects CD CD again at P P then TP∥AD TP\parallel{}AD.
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