In triangle ABC, AB = AC = 13 and BC = 10. Let I be the incenter of triangle ABC. Compute lengths AI, BI, and CI.
+128474 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)
