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December 21, 2014

December 21, 2014

Posted by **v** on Tuesday, June 8, 2010 at 7:03am.

- geometry -
**Reiny**, Tuesday, June 8, 2010 at 7:57ammake a diagram

Triangle ABC with AB=17, BC=8 and AC = 15

Did you realize that your triangle is right-angled, with angle C = 90° ?

let the points of contact of the circle be

D on BC, E on AC, and F on AB

Two properties we can use ...

1. The centre of the incscribed circle lies on the angle bisectors of the triangle, and

2. BF=BC , AE=AF, and DC = EC, by the tangent properties

let the radius be r,

since the 90° is bisected, DC = r

then BD= 8-r, and of course by #2 BF=8-r

then AF= 9+r and AE = 15-r

I see two similar triangles at the top, so

r/(9+r) = r/(15-r)

solve for r

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