2006 AMC 12B Problems/Problem 15
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Problem
Circles with centers and have radii 2 and 4, respectively, and are externally tangent. Points and are on the circle centered at , and points and are on the circle centered at , such that and are common external tangents to the circles. What is the area of hexagon ?
Solution
Draw the altitude from onto and call the point . Because and are right angles due to being tangent to the circles, and the altitude creates as a right angle. is a rectangle with bisecting . The length is and has a length of , so by pythagorean's, is .
, which is half the area of the hexagon, so the area of the entire hexagon is
See also
2006 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 14 |
Followed by Problem 16 |
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All AMC 12 Problems and Solutions |