Problem:
Circles with centers A and B have radii 3 and 8 , respectively. A common internal tangent intersects the circles at C and D, respectively. Lines AB and CD intersect at E, and AE=5. What is CD?
Answer Choices:
A. 13
B. 344​
C. 221​
D. 255​
E. 355​ Solution:
Radii AC and BD are each perpendicular to CD. By the Pythagorean Theorem,
CE=52−32​=4
Because â–³ACE and â–³BDE are similar,
CEDE​=ACBD​, so DE=CE⋅ACBD​=4⋅38​=332​
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