2005 AMC 12B Problems/Problem 14
This problem has not been edited in. If you know this problem, please help us out by. A circle having center , with , is tangent to the lines , and . What is the radius of this circle?
Let be the radius of the circle. Draw the two radii that meet the points of tangency to the lines . We can see that a square is formed by the origin, two tangency points, and the center of the circle. The side lengths of this square are and the diagonal is . The diagonal of a square is times the side length. Therefore, .