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Maximum Area of a Certain Quadrilateral

Given a quadrilateral ABCD with a fixed angle at A and fixed lengths for BC and CD. Determine (Construct) ABCD such that it has the maximum area.

That is, points B and D would be located on the respective rays of angle A so that BC and CD are the sides opposite angle A and the area is a maximum. For example, the following figure shows a quadrilateral satisfying the conditions but probably NOT with the maxmimum area.

Click here for a GSP sketch to explore this problem.

Hint