Question 48
Let $k$ be the incircle of $\triangle ABC$ with $AC \neq BC$, $I$ be the center of $k$ and let $D$, $E$ and $F$ be the tangent points of $k$ to the sides $AB$, $BC$ and $AC$, respectively.
a) If $S = CI \cap EF$, prove that $\triangle CDI \sim \triangle DSI$.
b) Let $M$ be the second intersection point of $k$ and $CD$. The tangent line to $k$ at $M$ intersects the line $AB$ at point $G$. Prove that $GS \perp CI$.
a) If $S = CI \cap EF$, prove that $\triangle CDI \sim \triangle DSI$.
b) Let $M$ be the second intersection point of $k$ and $CD$. The tangent line to $k$ at $M$ intersects the line $AB$ at point $G$. Prove that $GS \perp CI$.