1962 AHSME Problems/Problem 25
Given square with side feet. A circle is drawn through vertices and and tangent to side . The radius of the circle, in feet, is:
Let be the center of the circle and be the point of tangency of the circle and and let be the point of intersection of lines and Because of the symmetry, feet. Let the length of be . The length of is . By Pythagorean Theorem, . Because , , and are radii of the same circle, . So, . Squaring both sides, we obtain . Subtracting from both sides and adding , our equation becomes , so our answer is .