MathDB

Identity: incenter, altitude, inradii, circumradii.

Source: Spain National Olympiad 2009 (OME), Problem 2

January 2, 2010

geometryincentercircumcircleperimetergeometry proposed

Problem Statement

Let

ABC

be an acute triangle with the incircle

C(I,r)

and the circumcircle

C(O,R)

. Denote

D\in BC

for which

AD\perp BC

and AD \equal{} h_a . Prove that DI^2 \equal{} (2R \minus{} h_a)(h_a \minus{} 2r) .