MathNet 2026 — Part 10 Question 143

Given a circle $k$, let $AB$ be its diameter. An arbitrary line $l$ intersects the circle $k$ at the points $P$ and $Q$. If $A_{1}$ and $B_{1}$ are the feet of perpendiculars from $A$ and $B$ to $PQ$, prove that $A_{1}P = B_{1}Q$.