# An unrelated triangle

Geometry Level 4

Points $$A, B,$$ and $$C$$ are lying on a circle centered at $$P$$ such that $$AC$$ intersects $$BP$$ at $$D,$$ where $$AD=7, \angle APB\, (\alpha) = 120^{\circ},$$ and $$3[ADB]= 2[ADP].$$

If the area of $$\triangle CPD$$ can be expressed in the form $$\dfrac{a \sqrt{b}}{c}$$ for positive integers $$a, b,$$ and $$c$$ such that $$a,c$$ are coprime, and $$b$$ is square-free, determine $$a + b + c.$$


Notation: $$[\,\cdot\,]$$ denotes the area of the figure.

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