Question 54
We are given a right-angled triangle $MNP$ with right angle in $P$. Let $k_M$ be the circle with center $M$ and radius $MP$, and let $k_N$ be the circle with center $N$ and radius $NP$.
Let $A$ and $B$ be the common points of $k_M$ and the line $MN$, and let $C$ and $D$ be the common points of $k_N$ and the line $MN$, with $C$ between $A$ and $B$.
Prove that the line $PC$ bisects the angle $APB$.
Let $A$ and $B$ be the common points of $k_M$ and the line $MN$, and let $C$ and $D$ be the common points of $k_N$ and the line $MN$, with $C$ between $A$ and $B$.
Prove that the line $PC$ bisects the angle $APB$.