In triangle ABC, AB=5, AC=6, and BC=8. Circles are drawn with centers A, B, and C, so that any two circles are externally tangent. Find the sum of the areas of the circles.
+37165 AB = 5 ra + rb = 5 (ra = radius of circle 'a' etc)
AC = 6 ra + rc = 6
BC = 8 rb + rc = 8
solve for the radii then you can comput the areas
ra = 5 - rb sub into second equation
5-rb + rc = 6 multiply eq 3 by -1 and add to this equation to get:
5 - 2 rb = -2
rb = 3.5 the ra = 1.5 rc =4.5 <============Take it from here !
