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Concetric

Author: mathforces
Problem has been solved: 58 times

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The circles $ \omega_1 $ and $ \omega_2 $ are concentric and the ratio of the radius $ \omega_1 $ to the radius $ \omega_2 $ is $ \frac{1}{3} $. $ XY $ is the diameter of $ \omega_2 $, $ YZ $ is the tangent to $ \omega_1 $ ($ Z $ lies on $ \omega_2 $) and $ XZ = 12 $. Let $ r $ be the radius of $ \omega_2 $. What is $ [2020r] $ equal to?





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