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.
Burlingame, Peyton, "Cross Ratio" (2017). Paper Presentations. 2.