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MathNet 2026 — Part 06 Question 111

Math Olympiad Vault · MathNet 2026 — Part 06

Question 111

Let $ABCD$ be a square and let $\Gamma$ denote the circle with diameter $CD$. A tangent line is drawn to the circle $\Gamma$ from $B$, meeting the circle $\Gamma$ at $E$ and intersecting the segment $AD$ at $K$.
Prove that $|AD| = 4|KD|$.