tangential quad property
Source: Polish MO second round 1957 p6
August 29, 2024
tangentialgeometry
Problem Statement
Prove that if a convex quadrilateral has the property that there exists a circle tangent to its sides (i.e. an inscribed circle), and also a circle tangent to the extensions of its sides (an excircle), then the diagonals of the quadrilateral are perpendicular to each other.