Erdős-Mordell Theorem


If P is a pedal point inside a triangle DeltaABC, and P_A, P_B, and P_C are the feet of the perpendiculars from P upon the respective sides BC, CA, and AB, then


This inequality was proposed by Erdős (1935), and solved by Mordell and Barrow (1937) two years later. Elementary proofs were subsequently found by Kazarinoff in 1945 (Kazarinoff 1961, p. 78) and Bankoff (1958).

Oppenheim (1961) and Mordell (1962) also showed that


See also

Pedal Point

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Cite this as:

Weisstein, Eric W. "Erdős-Mordell Theorem." From MathWorld--A Wolfram Web Resource.

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