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trapezoid with points equidistant from the diagonals intersection

Source: All Russian MO 1994 ARO IX P7

July 29, 2018
geometrytrapezoid

Problem Statement

A trapezoid ABCDABCD (AB///CDAB ///CD) has the property that there are points PP and QQ on sides ADAD and BCBC respectively such that ∠APB=∠CPD\angle APB = \angle CPD and ∠AQB=∠CQD\angle AQB = \angle CQD. Show that the points PP and QQ are equidistant from the intersection point of the diagonals of the trapezoid.
(M. Smurov)
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