<ul><li>The Erdős-Mordell theorem states that from any interior point within a given triangle, the distances to the vertices are at least twice the distances to the sides.</li><li>The theorem was conjectured by Paul Erdős in 1935 and proved by Louis Mordell in the same year. It states that OA + OB + OC ≥ 2(OD + OE + OF), where O is the interior point and OA, OB, OC are the distances to the vertices, and OD, OE, OF are the distances to the sides.</li><li>The theorem holds true for any triangle, and equality occurs only when the triangle is equilateral.</li><li>Hojoo Lee provided an elementary proof of the Erdős-Mordell theorem in 2001. There is also a generalized version of the theorem that involves weighted distances to the vertices and sides.</li></ul>

Erdős-Mordell triangle theorem

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