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angle bisector is wanted, circle through A tangent to BC related

Source: Mathematics Regional Olympiad of Mexico Center Zone 2015 P2

November 12, 2021
geometryangle bisector

Problem Statement

In the triangle ABCABC, we have that ∠BAC\angle BAC is acute. Let Γ\Gamma be the circle that passes through AA and is tangent to the side BCBC at CC. Let MM be the midpoint of BCBC and let DD be the other point of intersection of Γ\Gamma with AMAM. If BDBD cuts back toΓ \Gamma at EE, show that ACAC is the bisector of ∠BAE\angle BAE.
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