See complete Problem 81

Triangle Area, Side, Inradius, Circumradius. Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.

## Monday, May 19, 2008

### Elearn Geometry Problem 81

Labels:
area,
circumcircle,
circumradius,
incircle,
inradius,
side,
triangle

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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