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# What is the diameter of the circle inscribed in triangle \$ABC\$ if \$AB = 11, AC=6, BC=7\$? Express your answer in simplest radical form.

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What is the diameter of the circle inscribed in triangle \$ABC\$ if \$AB = 11, AC=6, BC=7\$? Express your answer in simplest radical form.

RektTheNoob  Nov 29, 2017
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The semi-perimeter, s, of this triangle  is    [ 6 + 7 + 11 ] / 2  =  12

The area, K  =     √  [ s  (s - a) (s - b) (s -c)  ]    where a,b, c are the sides...so we have

K  = √  [ 12  ( 12 - 11) (12 - 7) (12 - 6) ]  =  √ [12 * 5 * 6 ]  = √ 360  = 6√10

And we can solve for the  inradius, r, as  :

K  =  r * s

6√10  =  r  *  12         divide both sides by 12

√10 / 2   =  r     = the inradius

And the diameter is twice this  =  √10  units

CPhill  Nov 29, 2017

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