SOLUTION: Find the percentage of the area of a circle that is contained in an inscribed isosceles triangle, one of those sides is the diameter of the circle

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Question 1108307: Find the percentage of the area of a circle that is contained in an inscribed isosceles triangle, one of those sides is the diameter of the circle
Answer by greenestamps(13203) About Me  (Show Source):
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The area of the circle is pi times the radius squared: A+=+pi%2Ar%5E2.

The triangle is isosceles with one side being the diameter of the circle. That means the triangle is an isosceles right triangle with hypotenuse equal to two times the radius. That makes the legs of the triangle each the square root of 2 times the radius. Finally the area of the triangle is one-half base time height, with the two legs being the base and height: A+=+%281%2F2%29%28r%2Asqrt%282%29%29%5E2+=+%281%2F2%29%2A2r%5E2+=+r%5E2.

So the fraction of the area of the circle that is inside the triangle is %28r%5E2%29%2F%28pi%2Ar%5E2%29+=+1%2Fpi.

Convert that answer to a percentage using a calculator.