IIT JEE , AIEEE Forum - Mathematics , Trignometry

deepesh28

in triangle ABC Ra,Rb,Rc R THE RADII OF THE CIRCLES WHICH TOUCHTHE INCIRCLE ND THE SIDES EMANTING FROM THE VERTICES A,B,C RESPECTIVELY .PROVE THAT

(Ra.Rb)^1/2 +(Rb.Rc)^1/2 +(Rc.Ra)^1/2 =r

Decoder

good question yaar!! but afsos no one tried!!

i did this with geometry..
i m getting r/3 on the other side....

while with trigo it is r..surely..

ayshwarya

let Ra=r1 we know r1=4RsinA/2xcosB/2xcosC/2
similarly Rb=r2=4 Rcos A/2xsinA/2xcosC/2
Rc=r3=4RcosA/2xcosB/2XsinC/2
on solving we get lhs=rhs

deepesh28

no Ra is not R1