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SMO 2013 Senior Round 1 Question 25

SMO · SMO 2013 Senior Round 1

Question 25

As shown in the figure below, circles $C_1,C_2$ of radius $360$ are tangent to each other and both tangent to straight line $\ell$. If circle $C_3$ is tangent to $C_1,C_2,\ell$, and circle $C_4$ is tangent to $C_1,C_3,\ell$, find the radius of $C_4$.

Question illustration