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

radiusof-the-circle
length-of-the-square

#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?

Answer:

the point of tangency is the middle of the side

the chord perpendicular to the tangent is a diameter

the height of the right triangle in the semicircle is half of the side of the square

the length of the diameter is 2½ … the radius is 1¼