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Problem 5 of Finals

Source: I International Festival of Young Mathematicians Sozopol 2010, Theme for 10-12 grade

December 16, 2019
geometryexcircle

Problem Statement

We are given ΔABC\Delta ABC, for which the excircle to side BCBC is tangent to the continuations of ABAB and ACAC in points EE and FF respectively. Let DD be the reflection of AA in line EFEF. If it is known that ∠BAC=2∠BDC\angle BAC=2\angle BDC, then determine ∠BAC\angle BAC.
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