Trigonometry/For Enthusiasts/Erdős–Mordell inequality

In Euclidean geometry, the Erdős–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. It is named after Paul Erdős and Louis Mordell. posed the problem of proving the identity; a proof was provided two years later by. This solution was however not very elementary. Subsequent simpler proofs were then found by, , and.

In absolute geometry, the Erdős–Mordell inequality is equivalent to the statement that the sum of the angles of a triangle is at most 2$$\pi$$.