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What is the radius of the circle inscribed in triangle $ABC$ if $AB = 12,$ $AC=14,$ $BC=20$? Express your answer in simplest radical form.

 Oct 12, 2023
 #1
avatar+128732 
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semi-perimeter, s ,  =    (12 + 14 + 20)   / 2 =    23

 

radius of incircle  =   sqrt  [   ( 23 - 12) (23 - 14) (23 - 20)  / 23 ]  = sqrt   [ 11 * 9 * 3 /  23 ] = sqrt (297 / 23) =

 

3 sqrt (33/23)  =   (3/23) sqrt (33 * 23)  =   (3/23)sqrt (759)  

 

 

cool cool cool

 Oct 12, 2023

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