Geometric Artwork of Problem 1072. Triangle and Altitudes. PicSketch for iPad

Geometric Art of Problem 1072. Triangle and the Altitudes. iPad apps.

The figure above shows a triangle ABC with an interior point P and the altitudes h_a, h_b, and h_c. If p_a, p_b, and p_c are the distances from P to the sides, prove that p_a / h_a + p_b / h_b + p_c / h_c = 1. See also: Problem 1072.