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Source: Spain Mathematical Olympiad 2021 P1

May 10, 2021
geometry3D geometrySpaintrigonometry

Problem Statement

Vertices A,B,CA, B, C of a equilateral triangle of side 11 are in the surface of a sphere with radius 11 and center OO. Let DD be the orthogonal projection of AA on the plane α\alpha determined by points B,C,OB, C, O. Let NN be one of the intersections of the line perpendicular to α\alpha passing through OO with the sphere. Find the angle ∠DNO\angle DNO.
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