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Bisection of an angle

Source: Iran TST 2008

July 5, 2008
geometrycircumcirclegeometric transformationreflectionsymmetryincenterangle bisector

Problem Statement

In the acute-angled triangle ABC ABC, D D is the intersection of the altitude passing through A A with BC BC and Ia I_a is the excenter of the triangle with respect to A A. K K is a point on the extension of AB AB from B B, for which \angle AKI_a\equal{}90^\circ\plus{}\frac 34\angle C. IaK I_aK intersects the extension of AD AD at L L. Prove that DIa DI_a bisects the angle ∠AIaB \angle AI_aB iff AL\equal{}2R. (R R is the circumradius of ABC ABC)
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