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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