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Competitive Stats
Q29Section II (Mathematics)29 of 84

Four points are concyclic or collinear iff their cross ratio is real

The complex numbers z1,z2,z3,z4z_1,z_2,z_3,z_4 are either collinear or they lie on a circle if their cross ratio z1−z3z2−z3⋅z2−z4z1−z4\dfrac{z_1-z_3}{z_2-z_3}\cdot\dfrac{z_2-z_4}{z_1-z_4} is:

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