MathDB
Altitude

Source:

May 24, 2006
geometrytrigonometry

Problem Statement

Let ABCABC be a triangle with AB=ACAB = AC and let DD be a point on BCBC such that the incircle of ABDABD and the excircle of ADCADC corresponding to AA have the same radius. Prove that this radius is equal to one quarter of the altitude from BB of triangle ABCABC.