Math CentralQuandaries & Queries


Question from Sobeida, a student:

A rectangle that is x feet wide is inscribed in a circle of radius 8 feet. What is the area of the rectangle as a function of x.


Hello Sobeida,

Try drawing a rectangle inscribed in a circle. Then divide the rectangle into four equal smaller rectangles, by bisecting each side. Finally, draw a radius from the center of the circle (this will be the center of the rectangle too) to a corner of the rectangle on the circumference of the circle.

Can you convince yourself that you have eight congruent right triangles?

Can you manipulate the Pythagorean formula to find an expression for the area of one right triangle given x?

If so, just multiply by eight.

Stephen La Rocque.

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