Problem

Source: India IMOTC Practice Test 2 Problem 3

Tags: geometry



Let ABCD be a convex quadrilateral which admits an incircle. Let AB produced beyond B meet DC produced towards C, at E. Let BC produced beyond C meet AD produced towards D, at F. Let G be the point on line AB so that FGCD, and let H be the point on line BC so that EHAD. Prove that the (concave) quadrilateral EGFH admits an excircle tangent to ¯EG,¯EH,FG,FH. Proposed by Rijul Saini