2

Part of 2009 Spain Mathematical Olympiad

Problems(1)

Identity: incenter, altitude, inradii, circumradii.

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

ABC

be an acute triangle with the incircle

C(I,r)

and the circumcircle

C(O,R)

D\in BC

AD\perp BC

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

geometryincentercircumcircleperimetergeometry proposed