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X(1), X(2), X(9), X(10), X(37), X(226), X(281), X(1214) midpoints of ABC 

The hexyl triangle is the reflection in O of the excentral triangle IaIbIc. See also TCCT p.172. K345 is the locus of P whose anticevian triangle is orthologic to either of the intouch, excentral or hexyl triangles. K345 is the isogonal transform of K319. It is anharmonically equivalent to the Thomson cubic. See Table 21 and also K168.
The anticevian triangle of any point on K345 is perspective with the outer Garcia triangle (see ETC, preamble of X5587) and the perspector lies on K033. 
