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Erdős-Mordell Inequality
Statement
The Erdős-Mordell theorem states that if P is a pedal point inside a triangle ΔABC 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 PA + PB + PC>=2(PP_A + PP_B + PP_C).
Alternate name
History
formulation date | 1935 (91 years ago) formulator | Paul Erdős status | proved proof date | 1937 (2 years later) (89 years ago) provers | Louis Joel Mordell | David Francis Barrow additional people involved | Donat Kazarinoff | Leon Bankoff
Associated equation
PA + PB + PC>=2(PP_A + PP_B + PP_C)
Current evidence
Elementary proofs were obtained by Kazarinoff and Bankoff.