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In triangle ABC, AB = AC = 13 and BC = 10.  Let I be the incenter of triangle ABC.  Compute lengths AI, BI, and CI.

 Dec 12, 2020
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See the image here

 

A = (5,12)   B  =(0,0)      C  = ( 10,0)

 

Calculation of  x coordinate of  incenter

 

(x coordinate  of A *  side length opposite of A  +  x coordinate of B *side  length opposite B  +  x coordinate of C * side length opposite C )  /Perimeter

 

So we  have  ( 5*10  + 0   + 10*13 ) / 36   =   180/36  = 5

 

Similarly  the  y coordinate of the  incenter is  =

 

(12*10  + 0  +  0*13)    / 36  =    ( 120 ) /36    =  10/3

 

AI =    sqrt  [ (12 - 10/3)^2 ] =  26/3

BI =  CI  =  sqrt  ( 5^2  + (10/3)^2 ] =  sqrt  [ 225/9 + 100/9 ]  =  sqrt  [ 325] /3  = (5/3)sqrt ( 13)

 

 

 

cool cool cool

 Dec 13, 2020

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