2018 AMC 10A Problems/Problem 15
Two circles of radius 5 are externally tangent to each other and are internally tangent to a circle of radius 13 at points and , as shown in the diagram. The distance can be written in the form , where and are relatively prime positive integers. What is ?
Solution
Call center of the largest circle . The circle that is tangent at point will have point as the center. Similarly, the circle that is tangent at point will have point as the center. Connect , , , and . Now observe that is similar to . Writing out the ratios, we get Therefore, our answer is , which is choice .
~Nivek
2018 AMC 10A (Problems • Answer Key • Resources) | ||
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