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Geometry Level 5

A sphere of radius 11 is tangent to the plane Π\Pi at the point A.A. A line l,l, that makes an angle ϕ\phi with Π,\Pi, intersects Π\Pi at a point C.C. It is tangent to the sphere at a point B.B. The length of ACAC is 22 and tanϕ=512.\tan \phi = \frac{5}{12}. The square of the length of ABAB can be written as ab,\frac{a}{b}, where aa and bb are coprime positive integers. What is a+b?a+b?

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