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equal quadrilaterals, cyclic, _|_ diag., orthocenters (2010 Kyiv City MO 11.3)

Source:

July 13, 2020
geometrycongruentinscribedorthocenter

Problem Statement

The quadrilateral ABCDABCD is inscribed in a circle and has perpendicular diagonals. Points K,L,M,QK,L,M,Q are the points of intersection of the altitudes of the triangles ABD,ACD,BCD,ABCABD, ACD, BCD, ABC, respectively. Prove that the quadrilateral KLMQKLMQ is equal to the quadrilateral ABCDABCD.
(Rozhkova Maria)
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