1982 AHSME Problems/Problem 14
In the adjoining figure, points and lie on line segment , and , and are diameters of circle , and , respectively. Circles , and all have radius and the line is tangent to circle at . If intersects circle at points and , then chord has length
Since is 15, is 75, and , .
Now drop a perpendicular from to at point . , and since is similar to . . so by the Pythagorean Theorem, . Thus Answer is then .