If
is a pedal point inside a triangle , and , , and are the feet of the perpendiculars from upon the respective sides , , and , 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
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