Problem:
A circle of radius has center at . A circle of radius has center at . A line is tangent to the two circles at points in the first quadrant. Which of the following is closest to the -intercept of the line?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let and denote the centers of the circles. Let and be the points where the -axis and -axis intersect the tangent line, respectively. Let and denote the points of tangency as shown. We know that , , and . Let and . Triangles and are similar, so
which yields . Hence, . Also, triangles and are similar,
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