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Coxeter - Excercise 3.1.2

Let the diagonal points of a quadrangle PQRS be A, B, and C. Respectively the intersections of PS and QR, QS and RP, and RS and PQ. Define the further intersections A_1, A_2, A_3, B_1, B_2, B_3, C_1, C_2, and C_3 as shown in the picture. A_1B_2C_2, A_2B_1C_2, A_2B_2C_1, and A_1B_1C_1 are triads of points that lie on the lines pqrs forming the quadrilateral pqrs whose three diagonal lines are the sids a = BC, b = CA, and c = AB. The quadrangle PQRS and the quadrilateral pqrs have the same diagonal triangle.