Problem

Source:

Tags: geometry, incenter, geometric transformation, circumcircle, reflection, inradius, IMO Shortlist



Let $I$ be the incentre of a triangle $ABC$ and $\Gamma_a$ be the excircle opposite $A$ touching $BC$ at $D$. If $ID$ meets $\Gamma_a$ again at $S$, prove that $DS$ bisects $\angle BSC$.