MathDB
property of intersection point of diagonals in a cyclic ABCD (distance ratio)

Source: Sharygin 2005 finals 11.3

August 31, 2019
ratiodistancecyclic quadrilateralgeometrydiagonals

Problem Statement

Inside the inscribed quadrilateral ABCDABCD there is a point KK, the distances from which to the sides ABCDABCD are proportional to these sides. Prove that KK is the intersection point of the diagonals of ABCDABCD.