A circle passes through two adjacent vertices of a square and is tangent to the opposite side of the square

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radius-the-circle

#1

A circle passes through two adjacent vertices of a square and is tangent to the opposite side of the square. If the side length of the square is 2 units, what is the radius of the circle? Please show how you get the answer.

Answer:

If you draw lines from the corners that the circle is touching up to 1.5 on the opposite side of the square, the intersection of those lines is the center of the circle. You can use Pythagorean Theorum to get diameter of the circle of 2.5. So radius is 1.25.