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MathNet 2026 — Part 03 Question 111

Math Olympiad Vault · MathNet 2026 — Part 03

Question 111

Let $r$ and $s$ be two parallel lines, and $A$ a fixed point at the same distance from both lines. For each $B$ point of the $r$, let $C$ be the point of the $s$ straight that $\angle B A C = 90^{\circ}$, and it is $P$ The perpendicular foot from $A$ on the straight $B C$. It shows that regardless of what point $B$ of the line $r$ we take, the point $P$ is on a fixed circumference.