MathDB

1

Part of 2002 Iran Team Selection Test

Problems(1)

Tangential quadrilateral

Source: Iran TST 2002

9/27/2006
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.
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