Cross Ratio

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A question posed in the MAA Monthly is the following: “Given four points A, B, C, and D in order on a line in Euclidean space, under what conditions will there be a point P off the line such that the angles ???APB, ?BPC, and ?CPD have equal measure.” We will present a partial solution of this question using the cross ratio. The cross ratio plays a central role in projective geometry however can be proved using the Law of Sines. The elements of the proofs are comprised of calculus, algebra, and geometry.

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Mathematics Commons



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