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X(21), X(256), X(846), X(1281), X(1284), X(1580), X(8424), X(8843), X(8844), X(8845), X(8846), X(8847), X(8852), X(8931), X(8932), X(8933), X(8934), X(16360), X(16362), X(16366)

vertices of the 1st Sharygin triangle A1B1C1

Geometric properties :

See K673 for explanations, also K132, K323 and K961, K962.

K960 meets the sidelines of A1B1C1 again at A1', B1', C1' and the triangles ABC and A1'B1'C1' are perspective at X(8852).

A1B1C1 and A1'B1'C1' are also perspective at X(1580). It follows that K960 is a pK with pivot X(1580), isopivot X(1281) with respect to A1B1C1.

The isopivot of K960 withe respect to ABC is Q = X(16366) = a (a^2-b c) / (a^4-a b^3-a^2 b c-2 b^2 c^2-a c^3) : : .