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MathNet 2025-part-01 — 187 problems (EN–VI) Question 52

Math Olympiad Vault · MathNet 2025-part-01 — 187 problems (EN–VI)

Question 52

The midpoint of the hypotenuse $AB$ of a right-angled triangle $ABC$ is $M$. A point $D$ lies on the side $BC$ such that the circumcircle of the triangle $ACD$ intersects the line $DM$ at some point $K$ between the points $D$ and $M$. Let $L$ be the reflection of the point $K$ from the point $M$. The circumcircles of the triangles $ACD$ and $LBC$ intersect at the point $N$, $N \neq C$. Find the size of the angle $KNL$.