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lines are angle bisectors of cyclic quad

Source: Polish MO Second Round 1950 p3

September 1, 2024
geometrycyclic quadrilateralangle bisector

Problem Statement

The diagonals of a quadrangle inscribed in a circle intersect at point KK. The projections of the point K K onto the subsequent sides of this quadrangle are points M,N,P,QM, N, P, Q. Prove that these lines KMKM, KNKN, KPKP, KQKQ are the angle bisectors of the quadrangle MNPQMNPQ.
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