Question 44
Let triangle $\triangle A B C$ be given. Point $P$ lies on segment $B C$ such that the circle with diameter $B P$ passes through the centre of the incircle of $\triangle A B C$. Prove that
$$
\frac{|B P|}{|P C|}=\frac{c}{s-c}
$$
where $c$ is the length of segment $A B$, and $s$ is half the perimeter of $\triangle A B C$.
$$
\frac{|B P|}{|P C|}=\frac{c}{s-c}
$$
where $c$ is the length of segment $A B$, and $s$ is half the perimeter of $\triangle A B C$.