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).

Erdős-Mordell inequality

formulation date | 1935 (90 years ago) formulator | Paul Erdős status | proved proof date | 1937 (2 years later) (88 years ago) provers | Louis Joel Mordell | David Francis Barrow additional people involved | Donat Kazarinoff | Leon Bankoff

PA + PB + PC>=2(PP_A + PP_B + PP_C)

Elementary proofs were obtained by Kazarinoff and Bankoff.

solved mathematics problems | mathematics theorems