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romanian angle chasing, circumcircle, incircle and angle bisectors related

Source: IMAC Arhimede 2013 p5

September 26, 2018
geometrycircumcircleincircleAngle Chasinganglesangle bisector

Problem Statement

Let Γ\Gamma be the circumcircle of a triangle ABCABC and let EE and FF be the intersections of the bisectors of ∠ABC\angle ABC and ∠ACB\angle ACB with Γ\Gamma. If EFEF is tangent to the incircle γ\gamma of △ABC\triangle ABC, then find the value of ∠BAC\angle BAC.
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