quadrilateral with _|_ diagonals, perpendiculars from intersection point
Source: Bulgaria 1972 P5
June 21, 2021
geometrycyclic quadrilateralperpendicularinequalitiesGeometric Inequalities
Problem Statement
In a circle with radius , there is inscribed a quadrilateral with perpendicular diagonals. From the intersection point of the diagonals, there are perpendiculars drawn to the sides of the quadrilateral.(a) Prove that the feet of these perpendiculars are vertices of the quadrilateral that is inscribed and circumscribed.
(b) Prove the inequalities where and are radii respectively of the circumcircle and inscircle to the quadrilateral . When does equality hold?H. Lesov