cyclic quad is rhombus
Source: Polish MO Finals 1951 p5
August 28, 2024
rhombusgeometrycyclic quadrilateral
Problem Statement
A quadrilateral is inscribed in a circle. The lines and intersect at point , and the lines and intersect at point . The bisector of the angle intersects the side at the point and the side at the point ; and the bisector of the angle intersects the side at the point and the side at the point . Prove that the quadrilateral is a rhombus.