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Math Help - Equicircles

  1. #1
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    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?
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  2. #2
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    Quote Originally Posted by abradfo1 View Post
    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?
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  3. #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
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  4. #4
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    Quote Originally Posted by abradfo1 View Post
    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.
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  5. #5
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    Talking

    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
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