The sum of the distances from any interior point to the sides of an equilateral triangle equals the length of the triangle's altitude

Triangle

Centroid

Centroid

Circumcenter

Incenter

Orthocenter

Euler Line

Gergonne Point

Ceva's Theorem

Ceva's Theorem

Isotomic Conjugate

Menelaus's Theorem

Napoleon's Theorem

Finsler-Hadwiger Theorem

Morley's Trisector Theorem

Viviani's Theorem

Van Aubel's Theorem

Thébault's I Problem

Fagnano's Problem

Droz-Farny Line Theorem

The sum of the distances from any interior point to the sides of an equilateral triangle equals the length of the triangle's altitude