Question 132
Let $ABC$ be a triangle with $AB \neq AC$. The points $K, L, M$ are the midpoints of the sides $BC, CA, AB$, respectively. The inscribed circle of $ABC$ with centre $I$ touches the side $BC$ at point $D$. The line $g$, which passes through the midpoint of segment $ID$ and is perpendicular to $IK$, intersects the line $LM$ at point $P$.
Prove that $\angle PIA = 90^{\circ}$.
Prove that $\angle PIA = 90^{\circ}$.