Monday, May 19, 2008

Elearn Geometry Problem 81



See complete Problem 81
Triangle Area, Side, Inradius, Circumradius. Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.

2 comments:

  1. We refer to the previous problem where it has been proven that S1 = (r^2/bc)*S. However, by standard triangle formula S = abc/4R where a, b & c have their usual meanings.
    Hence, S1 = (r^2/bc)*abc/4R = ar^2/4R
    Ajit: ajitathle@gmail.com

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  2. In Tr. DEI, let m be the length of the altitude from E.
    Let X be the midpoint of BC

    From similar triangles
    a/2R = m/r …(1),

    Now S1 = rm/2 …(2)

    (2)/(1) gives us S1/(a/2R) = r^2/2,

    Hence S1 = ar^2/4R

    Sumith Peiris
    Moratuwa
    Sri Lanka

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