Question 33
Let $\triangle ABC$ be a triangle. Let $P$ be a point on the segment $BC$, such that the circle with diameter $BP$ passes through the incentre of $\triangle ABC$. Prove that
$$
\frac{|BP|}{|PC|} = \frac{c}{s-c},
$$
where $c$ is the length of the segment $AB$, and $s$ is half the perimeter of $\triangle ABC$.
$$
\frac{|BP|}{|PC|} = \frac{c}{s-c},
$$
where $c$ is the length of the segment $AB$, and $s$ is half the perimeter of $\triangle ABC$.