Quad sandwiched between confocal ellipses
Source: Shargyin 2022
March 4, 2022
conicsellipsegeometry
Problem Statement
An ellipse with focus is given. Two perpendicular lines passing through meet the ellipse at four points. The tangents to the ellipse at these points form a quadrilateral circumscribed around the ellipse. Prove that this quadrilateral is inscribed into a conic with focus