The following figure shows a quadrilateral with sides a,
Chapter 9, Problem 53(choose chapter or problem)
The following figure shows a quadrilateral with sides a, b, c, and d inscribed in a circle. If l denotes the length of the diagonal indicated in the figure, prove that This result is known as Brahmaguptas theorem. It is named after its discoverer, a seventh-century Hindu mathematician. Hint: Assume as given the theorem from geometry stating that when a quadrilateral is inscribed in a circle, the opposite angles are supplementary. Apply the law of cosines in both of the triangles in the figure to obtain expressions for l2 . Then eliminate cos u from one equation.
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