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ad= bc, distances from a point of circumcircle to lines of inscribed ABCD

Source: 2021 Oral Moscow Geometry Olympiad grades 10-11 p1

May 24, 2021
geometrycircumcirclecyclic quadrilateral

Problem Statement

Quadrilateral ABCDABCD is inscribed in a circle, EE is an arbitrary point of this circle. It is known that distances from point EE to lines AB,AC,BDAB, AC, BD and CDCD are equal to a,b,ca, b, c and dd respectively. Prove that ad=bcad= bc.
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