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MathNet 2026 — Part 04 Question 13

Math Olympiad Vault · MathNet 2026 — Part 04

Question 13

Let $\Omega$ and $\Gamma$ two secant circles. we note $A$ one of their intersections. Let $d$ any straight line passing through the point $A$. we note $P$ and $Q$ the respective intersections of the line $d$ with the circles $\Omega$ and $\Gamma$ different from $A$. Show that there is a point independent of the line $d$ chosen and which always belongs to the perpendicular bisector of the segment $[PQ]$.

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