A very long name

Geometry Level 3

a+b+cd=16a+bc+d=30ab+c+d=35a+b+c+d=42 \begin{aligned} a+b+c-d &=& 16 \\ a+b-c+d &=& 30 \\ a-b+c+d &=& 35 \\-a+b+c+d &=& 42 \end{aligned}

If constants a,b,c,da,b,c,d satisfy the system of equations above, find the area of a cyclic quadrilateral with sides a,b,c,da,b,c,d.

Inspiration

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