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3 circles, tangents, intersections, midpoint wanted

Source: Dutch 2013 IMO TST1 p3

August 2, 2019
geometrycirclesTangentsmidpoint

Problem Statement

Fix a triangle ABCABC. Let Γ1\Gamma_1 the circle through BB, tangent to edge in AA. Let Γ2\Gamma_2 the circle through C tangent to edge ABAB in AA. The second intersection of Γ1\Gamma_1 and Γ2\Gamma_2 is denoted by DD. The line ADAD has second intersection EE with the circumcircle of △ABC\vartriangle ABC. Show that DD is the midpoint of the segment AEAE.
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