Heron and Bretschneider

The Heron relation gives triangle area as a function of sides a, b, c.
Naming p the half perimeter p = (a+b+c)/2
 S = √( p(p-a)(p-b)(p-c) ) 
This relation is generalized for quadrilateral into Bretschneider relation :
 S = √( (p-a)(p-b)(p-c)(p-d) - abcd.cos²((B+D)/2) ) 

Application :

A parallelogram is such that its vertices are distant from a common internal point P by 1, 4, 7, 8
Maximal area of this parallelogram ? Solution
Construction ?
Details

 

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