One theorem to rule them all... do you know what it is?

Geometry Level 3

ABC is a triangle where AC is of length 13, and AB is of length 15. Point D is constructed on side CB such that the ratio CD:DB=12CD:DB=\frac{1}{2}. Let the cevian AD be of length 6. If CD can be expressed asa6\frac{\sqrt{a}}{\sqrt{6}}, find aa.

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