MathDB

5

Part of 2002 India Regional Mathematical Olympiad

Problems(1)

A cyclic quad

Source: Indian RMO 2002 Problem 5

10/27/2005
The circumference of a circle is divided into eight arcs by a convex quadrilateral ABCDABCD with four arcs lying inside the quadrilateral and the remaining four lying outside it. The lengths of the arcs lying inside the quadrilateral are denoted by p,q,r,sp,q,r,s in counter-clockwise direction. Suppose p+r=q+sp+r = q+s. Prove that ABCDABCD is cyclic.