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Relationship between circumradius and perpendicular in acute triangle

Source: Problem 2 from Regional Olympiad of Mexico Southeast 2024

September 29, 2024
geometrycircumradiusacute triangleperpendicularMexico

Problem Statement

Let ABCABC be an acute triangle with circumradius RR. Let DD be the midpoint of BCBC and FF the midpoint of ABAB. The perpendicular to ACAC through FF and the perpendicular to BCBC through BB intersect at NN. Prove that ND=RND = R.
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