In geometry, the polar circle of a triangle is the circle whose center is the triangle's orthocenter and whose squared radius is where A, B, C denote both the triangle's vertices and the angle measures at those vertices; H is the orthocenter ; D, E, F are the feet of the altitudes from vertices A, B, C respectively; R is the triangle's circumradius ; and a, b, c are the lengths of the triangle's sides opposite vertices A, B, C respectively.
