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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- Apr 21st 2008, 04:52 PM #1

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- Apr 22nd 2008, 12:02 PM #2

- Apr 22nd 2008, 12:12 PM #3

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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

- Apr 22nd 2008, 12:52 PM #4
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.

- Apr 22nd 2008, 03:08 PM #5

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