MathDB
cyclic quad is rhombus

Source: Polish MO Finals 1951 p5

August 28, 2024
rhombusgeometrycyclic quadrilateral

Problem Statement

A quadrilateral ABCD ABCD is inscribed in a circle. The lines ABAB and CDCD intersect at point EE, and the lines ADAD and BCBC intersect at point FF. The bisector of the angle AEC AEC intersects the side BC BC at the point M M and the side AD AD at the point N N ; and the bisector of the angle BFD BFD intersects the side AB AB at the point P P and the side CD CD at the point Q Q . Prove that the quadrilateral MPNQMPNQ is a rhombus.