SOLUTION: Five (5) externally tangent circles have their radius length equal 1 inch and their centers lie on the diagonal of a square. In addition, the two outer circles are tangent to two

Algebra ->  Circles -> SOLUTION: Five (5) externally tangent circles have their radius length equal 1 inch and their centers lie on the diagonal of a square. In addition, the two outer circles are tangent to two      Log On


   

Question 1180552: Five (5) externally tangent circles have their radius length equal 1 inch and their centers lie on the diagonal of a
square. In addition, the two outer circles are tangent to two sides of the square. Compute for the area outside the
circles but inside the square.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Draw a sketch of the circles aligned on the diagonal of the square.

Consider points A and B, which are the centers of the two circles in the corners of the square.

Each of those points is 1 unit from each side of the square; and the length of AB is 8 units. AB is the hypotenuse of an isosceles right triangle. Use those pieces of information to find the length of the side of the square.

Then the answer to the problem is the area of the square, minus the area of the 5 circles with radius 1.

If you need help finishing the problem, re-post, showing any work you have done and telling us where you are having difficulty.