High Quality Content by WIKIPEDIA articles! In Euclidean geometry, the Erd?s–Mordell inequality states that for any triangle ABC and point O inside ABC, the sum of the distances from O to the sides is less than or equal to half of the sum of the distances from O to the vertices. The inequality was conjectured by Erd?s as problem 3740 in the American Mathematical Monthly, 42 (1935). A proof was offered two years later by Mordell and Barrow. These solutions were however not very elementary. Subsequent simpler proofs were then found by Kazarinoff (1957) and Bankoff (1958).

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