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Quadrilateral $$ABCD$$ is inscribed in a circle with segment $$AC$$ a diameter of the circle. If $$m\angle DAC = 30^\circ$$ and $$m\angle BAC = 45^\circ$$, the ratio of the area of $$ABCD$$ to the area of the circle can be expressed as a common fraction in simplest radical form in terms of $$\pi$$ as $$\frac{a+\sqrt{b}}{c\pi}$$, where $$a$$$$b$$ and $$c$$ are positive integers. What is the value of $$a + b + c$$?

Mar 25, 2021