# Three in One

Geometry Level 4

A cyclic quadrilateral has side lengths of 5, 6, 7 and 8. Suppose $$S$$ represents the area of the quadrilateral, $$P$$ represents the area of its circumcircle and $$Q$$ represents the area of its inscribed-circle. Determine the value of $$\lfloor{S+P+Q}\rfloor$$.

You may use the approximation of $$\pi\approx3.1416$$.

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