Problem:
A triangle with side lengths in the ratio is inscribed in a circle of radius . What is the area of the triangle?
Answer Choices:
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Solution:
Let the sides of the triangle have lengths , and . The triangle is a right triangle, so its hypotenuse is a diameter of the circle. Thus , so . The area of the triangle is
A right triangle with side lengths 3,4 , and 5 has area . Because the given right triangle is inscribed in a circle with diameter 6 , the hypotenuse of this triangle has length 6 . Thus the sides of the given triangle are as long as those of a triangle, and its area is times that of a triangle. The area of the given triangle is
The problems on this page are the property of the MAA's American Mathematics Competitions