SOLUTION: Let a quadrilateral be given with sides a, b, c, and d. Suppose the quadrilateral is cyclic, and that it also has a circle inscribed in it. Show that its area is given by sqrt(abc

Question 419596: Let a quadrilateral be given with sides a, b, c, and d. Suppose the quadrilateral is cyclic, and that it also has a circle inscribed in it. Show that its area is given by sqrt(abcd).
Brahmagupta's Formula
Area^2=(s-a)(s-b)(s-c)(s-d), where s is the semi perimeter.
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
I don't recall the formula (maybe I just haven't seen it. Note that the quadrilateral must be able to have circles inscribed and circumscribed around it). I am pretty familiar with Brahmagupta's formula, which is a special case of Bretschneider's formula (the area of any quadrilateral with known interior angles).

The proof is somewhat lengthy, so I won't post one here. However, Wikipedia has some good articles about Bretschneider's and Brahmagupta's formulas, including their proofs, so I'll post them here:

http://en.wikipedia.org/wiki/Bretschneider's_formula
http://en.wikipedia.org/wiki/Brahmagupta%27s_formula

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