See complete Problem 81
Triangle Area, Side, Inradius, Circumradius. Level: High School, SAT Prep, College geometry
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Monday, May 19, 2008
Elearn Geometry Problem 81
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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.
ReplyDeleteHence, S1 = (r^2/bc)*abc/4R = ar^2/4R
Ajit: ajitathle@gmail.com
In Tr. DEI, let m be the length of the altitude from E.
ReplyDeleteLet 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