Question 4
Let $ABC$ be a non-isosceles triangle inscribed in a circle $\Gamma$ of radius $R$. The circle through $A$ tangent to $BC$ at $C$ meets again at $D$ the circle through $B$ tangent to $AC$ at $C$.
a) Prove that $CD\leq R$.
b) Prove that as $C$ moves on $\Gamma$, the line $CD$ passes through a fixed point.
a) Prove that $CD\leq R$.
b) Prove that as $C$ moves on $\Gamma$, the line $CD$ passes through a fixed point.