Circle Geometry re-visited .

[jay_shark]

Given a circle with radius R and an inscribed triangle ABC with inradius r , show that r= 4Rsin(A/2)sin(B/2)sin(C/2) .

The shorter the solution , the better !!

[TomCowley]

http://www.cut-the-knot.org/triangle...ngle.shtml#p4R

Just a bunch of double-angle manipulations, really. It takes 10 seconds to derive r=abc/4Rp which is just as simple.