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Question

Isosceles right triangle ABC encloses a semicircle of area 2. The circle has its center O on hypotenuse AB and is tangent to sides AC and BC. What is the area of triangle ABC? FIGURE

Accepted Answer

First, we notice half a square so first let's create a square. Once we have a square, we will have a full circle. This circle has a diameter of 4 which will be the side of the square. The area would be 4 4 = 16. Divide 16 by 2 to get the original shape and you get 8