SOLUTION: In triangle $XYZ,$ circles are drawn centered at $X$, $Y$, and $Z$, so that all pairs of circles are externally tangent. If $XY = 2,$ $XZ = 2,$ and $YZ = 2$, then find the sum of t

Algebra ->  Geometry-proofs -> SOLUTION: In triangle $XYZ,$ circles are drawn centered at $X$, $Y$, and $Z$, so that all pairs of circles are externally tangent. If $XY = 2,$ $XZ = 2,$ and $YZ = 2$, then find the sum of t      Log On


   

Question 1210548: In triangle $XYZ,$ circles are drawn centered at $X$, $Y$, and $Z$, so that all pairs of circles are externally tangent. If $XY = 2,$ $XZ = 2,$ and $YZ = 2$, then find the sum of the areas of all three circles.
Answer by greenestamps(13305) About Me  (Show Source):
You can put this solution on YOUR website!


From the description, triangle XYZ is equilateral with side length 2.

If circles drawn from each vertex are pairwise externally tangent, then each circle has radius 1.

So the area of each circle is pi, and the sum of the areas of the three circles is 3pi.

ANSWER: 3pi