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What is the radius of the circle inscribed in triangle $ABC$ if $AB = 12, AC=14, BC=16$? Express your answer in simplest radical form.

 Mar 3, 2021
 #1
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r =  2 * area  / perimeter

 

semi-perimeter,  S    =   (12 + 14 + 16)   / 2   =  21

 

Area  =  sqrt  [ 21  ( 21 - 16) (21 - 14) ( 21 -12) ]  =

 

sqrt [ 21 * 5 * 7 * 9 ]   =  21sqrt (15)

 

r  =  2 * 21 sqrt (15)  / 42  =   sqrt (15)

 

 

cool cool cool

 Mar 3, 2021

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