Problem

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Tags: geometry, circumcircle, incenter, ratio, trigonometry, cyclic quadrilateral, geometry proposed



Let $ ABC$ be a triangle and $ AB\ne AC$ . $ D$ is a point on $ BC$ such that $ BA = BD$ and $ B$ is between $ C$ and $ D$ . Let $ I_{c}$ be center of the circle which touches $ AB$ and the extensions of $ AC$ and $ BC$ . $ CI_{c}$ intersect the circumcircle of $ ABC$ again at $ T$ . If $ \angle TDI_{c} = \frac {\angle B + \angle C}{4}$ then find $ \angle A$