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Russian geometry problem

Source: Tuymaada 2016, Senior League/ P6 and P7 for juniors

July 22, 2016
geometry

Problem Statement

The numbers aa, bb, cc, dd satisfy 0<a≤b≤d≤c0<a \leq b \leq d \leq c and a+c=b+d{a+c=b+d}. Prove that for every internal point PP of a segment with length aa this segment is a side of a circumscribed quadrilateral with consecutive sides aa, bb, cc, dd, such that its incircle contains~PP.
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