Triangle in a circle

Geometry Level 2

Consider a circle with AB as its diameter. C is a point on the circumference of the circle and D is the foot of the altitude from C onto AB such that AD =\(\frac{CD}{2} \). If \(\frac{AD}{BD} \) = \(\frac{a}{b} \) where a and b are coprime positive integers, then a+b=?

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