MathDB
Tangential quadrilateral

Source: Iran TST 2002

September 27, 2006
geometrygeometry proposed

Problem Statement

ABCDABCD is a convex quadrilateral. We draw its diagnals to divide the quadrilateral to four triabgles. PP is the intersection of diagnals. I1,I2,I3,I4I_{1},I_{2},I_{3},I_{4} are excenters of PAD,PAB,PBC,PCDPAD,PAB,PBC,PCD(excenters corresponding vertex PP). Prove that I1,I2,I3,I4I_{1},I_{2},I_{3},I_{4} lie on a circle iff ABCDABCD is a tangential quadrilateral.
Back to ProblemsView on AoPS