Please help with circle tangents geometry

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Two circles of different sizes are tangent at T. A is on the smaller circle, whereas B is on the larger one. Also, segment CD is tangent to the smaller circle, and crosses the goes through the larger circle and hits the other side at D. TD is a diameter, and AB || CD. If the radius of the smaller circle is 2, what is the radius of the larger one?

I tried using perpendicular segments and right triangles, but they all seemed to fail. Could someone help? Thanks

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