Think rectangular in circular square!
Suppose we have a circle inscribed within a square. Now suppose a rectangle extends from one corner of the square to a point on the circle (see diagram).
If this rectangle is 6 inches by 12 inches, what is the radius of the circle in inches?
The answer is 30.
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1 solution
Construct a right angled triangle. Draw the hypotenuse from the point where the rectangle touches the circle to the center of the circle. Drop a vertical line down which meets the line from center of circle at right angle.
(r-12)^2+ (r-6)^2= r^2
solving it gives quadratic equation
r^2-36r+180=0
solving the equation r =30