SOLUTION: A circle of diameter 10 circumscribed by a right-angled isosceles triangle. Determine the perimeter of the triangle.

Question 320099: A circle of diameter 10 circumscribed by a right-angled isosceles triangle.
Determine the perimeter of the triangle.
Answer by CharlesG2(834) (Show Source): You can put this solution on YOUR website!
A circle of diameter 10 circumscribed by a right-angled isosceles triangle.
Determine the perimeter of the triangle.
circumscribe means that the circle will go around the right isosceles triangle with the corners of that triangle touching the edge of the circle
isosceles means that 2 of the sides of that triangle are equal
since the triangle is also a right triangle, that means the angles are 45-45-90, and the ratio of the sides is 1:1:sqrt(2)
and since the 90 degree angle on the triangle covers 1/2 the 360 degrees of arc of the circle, that means the diameter of the circle is also the hypotenuse of the triangle
so the side lengths of the triangle are both 10/sqrt(2) or (10sqrt(2))/2 or 5sqrt(2), added together that is 10sqrt(2)
perimeter of the isosceles right triangle is 10 + 10sqrt(2), or about 24.1

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