I have a homework problem that is supposed to deal with equicircles and all it says is:

Prove that Rr = (abc)/(4s)

Can anyone help me?

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- April 21st 2008, 05:52 PMabradfo1Equicircles
I have a homework problem that is supposed to deal with equicircles and all it says is:

Prove that Rr = (abc)/(4s)

Can anyone help me? - April 22nd 2008, 01:02 PMOpalg
- April 22nd 2008, 01:12 PMabradfo1
That's what Im not sure about... That's all the question say and I thought maybe that was a notation for a formula I'm totally missing.

I believe that a b and c are side of a triangle and r is a radius, so I'm guessing R is also a radius.

s i'm not sure about, its either a radius or a semi perimeter. There is no picture or explanation of any kind - April 22nd 2008, 01:52 PMOpalg
Ah yes, you're right: s is the semiperimeter. Also, r is the radius of the inscribed circle and R is the radius of the circumscribed circle. There's a formula saying that R=abc/4K, where K is the area of the triangle; and another formula saying that r=K/s. Put the two together and you get Rr=abc/4s, as required. Both formulas are given here (scroll down to the section "Scalene Triangle"), but without proof.

- April 22nd 2008, 04:08 PMabradfo1
That was very helpful! I knew that it had to do with putting to formulas together, but the ones on my sheet didn't match up. That link was very helpful, thank you