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2018 preRMO p29, angle chasing candidate, 2 incentres given

Source:

August 8, 2019
geometryincenterAngle Chasing

Problem Statement

Let DD be an interior point of the side BCBC of a triangle ABCABC. Let I1I_1 and I2I_2 be the incentres of triangles ABDABD and ACDACD respectively. Let AI1AI_1 and AI2AI_2 meet BCBC in EE and FF respectively. If ∠BI1E=60o\angle BI_1E = 60^o, what is the measure of ∠CI2F\angle CI_2F in degrees?
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