Question 118
The following figure shows a triangle $ABC$, right-angled at $C$, with a circle in its interior tangent to the three sides $AB$, $BC$ and $CA$ at the points $C_1$, $A_1$ and $B_1$, respectively. Let $H$ be the foot of the altitude to the side $A_1C_1$ of triangle $A_1B_1C_1$.
a) Compute the measure of the angle $\angle A_1C_1B_1$.
b) Show that the point $H$ lies on the bisector of the angle $\angle BAC$.
a) Compute the measure of the angle $\angle A_1C_1B_1$.
b) Show that the point $H$ lies on the bisector of the angle $\angle BAC$.