# Equicircles

• Apr 21st 2008, 04:52 PM
Equicircles
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?
• Apr 22nd 2008, 12:02 PM
Opalg
Quote:

Originally Posted by abradfo1
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?

I think you'll need to tell us what this notation means. Presumably a, b and c are the sides of a triangle, and I'm guessing that r, s and R are the radii of some of the circles that have the sides of the triangle as tangents?
• Apr 22nd 2008, 12:12 PM
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
Opalg
Quote:

Originally Posted by abradfo1
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

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