Problem: The straight line is divided at so that . Circles are described on and as diameters and a common tangent meets produced at . Then equals:
Answer Choices:
A. diameter of the smaller circle
B. radius of the smaller circle
C. radius of the larger circle
D.
E. the difference of the two radii.
Solution:
Let and let be the radius of the small circle. Draw the line from the center of each of the circles to the point of contact of the tangent and the circle.
By similar triangles,