1976 AHSME Problems/Problem 18
Problem 18
In the adjoining figure, is tangent at to the circle with center ; point is interior to the circle; and intersects the circle at . If , , and , then the radius of the circle is
Solution
Extend until it touches the opposite side of the circle, say at point By power of a point, we have so Therefore,
Now extend in both directions so that it intersects the circle in two points (in other words, draw the diameter of the circle that contains ). Let the two endpoints of this diameter be and where is closer to Again use power of a point. We have But if the radius of the circle is we see that and so we have the equation Solving gives