Question 141
The point $P$ is on the side $BC$ of triangle $ABC$. The incircles of $\triangle ABC$, $\triangle ABP$ and $\triangle ACP$ are denoted by $K$, $K_1$ and $K_2$, respectively.
Prove that the angle at which the radical axis of $K$ and $K_1$ meets the radical axis of $K$ and $K_2$ does not depend on the position of $P$. Find the measure of this angle if $\angle BAC = 100^\circ$.
Prove that the angle at which the radical axis of $K$ and $K_1$ meets the radical axis of $K$ and $K_2$ does not depend on the position of $P$. Find the measure of this angle if $\angle BAC = 100^\circ$.