# Too happening

Geometry Level 5

A sphere of radius $1$ is tangent to the plane $\Pi$ at the point $A.$ A line $l,$ that makes an angle $\phi$ with $\Pi,$ intersects $\Pi$ at a point $C.$ It is tangent to the sphere at a point $B.$ The length of $AC$ is $2$ and $\tan \phi = \frac{5}{12}.$ The square of the length of $AB$ can be written as $\frac{a}{b},$ where $a$ and $b$ are coprime positive integers. What is $a+b?$

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