Puzzles/Geometric Puzzles/Rectangle and Circle/Solution

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30 inches

Tools Used to Solve[edit]

Pythagorean Theorem

Quadratic Formula





We realize that every point on a circle is equidistant from the origin. This implies that the rectangle's corner touching the circle must be r inches away from the origin, where r is the radius. We can then draw a right triangle with sides and Now apply the Pythagorean Theorem to this triangle and solve for r.

The above equation is quadratic and can be solved by applying the Quadratic Formula.

Which simplifies to,

Now we can plug in our numbers and solve,


Thus the radius of our circle is 30 inches. Notice that 6 inches is not a valid answer. Why?

Comment: Simply making a statement that "we can then draw..." is confusing. Need more explanation on why r-x and r-y are valid descriptors for the triangle sides. This is easier to see with the r-x side than with the r-y.