Problem:
Externally tangent circles with centers at points and have radii of lengths and , respectively. A line externally tangent to both circles intersects ray at point . What is ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let and be the points of tangency to circles and , respectively, of the common tangent line that intersects ray at point . Then , and . Because right triangles and are similar, it follows that
so
Solving gives .
The problems on this page are the property of the MAA's American Mathematics Competitions