MathDB

4

Part of 2009 India IMO Training Camp

Problems(1)

India TST:Day2 Problem 1

Source: easy

5/16/2009
Let γ \gamma be circumcircle of △ABC \triangle ABC.Let Ra R_a be radius of circle touching AB,AC AB,AC&γ \gamma internally.Define Rb,Rc R_b,R_c similarly. Prove That \frac {1}{aR_a} \plus{} \frac {1}{bR_b} \plus{} \frac {1}{cR_c} \equal{} \frac {s^2}{rabc}.
geometrycircumcircletrigonometrygeometry proposed