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angle bisector wanted, internally tangent circles

Source: 2020 NZMO Round 2 p4

January 10, 2021
geometryangle bisectortangent circles

Problem Statement

Let Γ1\Gamma_1 and Γ2\Gamma_2 be circles internally tangent at point AA, with Γ1\Gamma_1 inside Γ2\Gamma_2. Let BCBC be a chord of Γ2\Gamma_2 which is tangent to Γ1\Gamma_1 at point DD. Prove that line ADAD is the angle bisector of ∠BAC\angle BAC.
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