MathDB

3

Part of 1950 Poland - Second Round

Problems(1)

lines are angle bisectors of cyclic quad

Source: Polish MO Second Round 1950 p3

9/1/2024
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.
geometrycyclic quadrilateralangle bisector