MathForces: Math Olympiads

# Concetric

Author: mathforces
Problem has been solved: 58 times

Русский язык | English Language

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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