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Romania Junior TST 2022 Day 3 P2

Source: Romania JBMO TST 2022

June 3, 2022
geometryromaniaRomanian TST

Problem Statement

Let C1\mathcal{C}_1 and C2\mathcal{C}_2 be two circles, internally tangent at PP (C2\mathcal{C}_2 lies inside of C1\mathcal{C}_1). A chord ABAB of C1\mathcal{C}_1 is tangent to C2\mathcal{C}_2 at C.C. Let DD be the second point of intersection between the line CPCP and C1.\mathcal{C}_1. A tangent from DD to C2\mathcal{C}_2 intersects C1\mathcal{C}_1 for the second time at EE and it intersects C2\mathcal{C}_2 at F.F. Prove that FF is the incenter of triangle ABE.ABE.
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