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In triangle ABC, AB = 17, AC = 25, BC = 28, and I is the incenter.  What is BI?

 Dec 31, 2020
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See the following image:

 

Let  B  =(0,0)     C  =(28,0)    A  = (8,15)

 

The x coordinate of the incenter    =   ( 0* 25 + 28*17 +  8*28)  / ( 17 + 25 + 28)    = 10

 

The y coordinate of the  incenter is  =   ( 0*25 + 0*17 + 15*28)  / ( 17 + 25 + 28)  =  6

 

So BI   =   sqrt  (10^2 + 6^2) =  sqrt (136) =  2sqrt (34)

 

 

cool cool cool

 Dec 31, 2020

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