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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.

 

 Dec 29, 2021
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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 !

 Dec 29, 2021

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