A circle passes through two adjacent vertices of a square and is tangent to one side of the
square. If the side length of the square is 2, what is the radius of the circle? Choose the correct choice from the following.
A) 3/2	B) 4 /3	C) 5 /4	D) 6 /5	E) None of these
Let A and B be the vertices through which the circle passes. LetM be the midpoint   of the line segment AB. The center C of the circle is on the line joining M to the midpoint of   the opposite side, which is also on the circle (see diagram below). Let r be the radius of the   circle. The length of the line segment joiningM to C is r-(2r-2) = 2-r as shown below.   Then 12+(2-r)2 = r2 by the Pythagorean Theorem. This gives 1+4-4r+r2 = r2, which   simplifies to 5- r = 0, so r = 5/4   correct answer 5 /4
<result>C</result>
A circle passes through two adjacent vertices of a square and is tangent to one side of the
square. If the side length of the square is 2, what is the radius of the circle?