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Pappus' Theorem

January 2001

Let $A_1, A_2, A_3, B_1, B_2, B_3 $ be six distinct points on the plane.

$ A_1, A_2 $ and $ A_3 $ are collinear, likewise $ B_1, B_2 $ and $ B_3 $.

Let $ C_1 $ be the intersection of the lines $ A_2B_3 $ and $ B_2A_3 $.

Let $ C_2 $ be the intersection of the lines $ A_3B_1 $ and $ B_3A_1 $.

Let $ C_3 $ be the intersection of the lines $ A_1B_2 $ and $ B_1A_2 $.

Then $ C_1, C_2 $ and $ C_3 $ are collinear.

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