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X(3), X(20), X(376), X(35237), X(67274), X(67275), X(67276)

infinite points of K243

points S1, S2, S3 of K243 on the circumcircle

points Q1, Q2, Q3 of nK0+(X3, X2) on the circumcircle

M1, M2, M3 midpoints of Q1Q2Q3

T1, T2, T3 projections of X(35237) on the sidelines of Q1Q2Q3

in/excenters of Q1Q2Q3 on the Stammler hyperbola

Geometric properties :

K1388 is the Thomson cubic of the triangle Q1Q2Q3 which is defined in the page K1386, the Simson-McCay cubic.

Most of the properties of K1386 still hold and are not repeated here.

K1388 passes through the midpoints M1, M2, M3 of Q1Q2Q3 and the tangents at these points the perpendicular bisectors of the triangle Q1Q2Q3.

The Steiner inellipse of Q1Q2Q3 is centered at X(376) and it is also inscribed in S1S2S3. It contains the six points M1, M2, M3, T1, T2, T3.

The tangents at Q1, Q2, Q3 to K1388 concur at X(35237) since it is the Lemoine point of Q1Q2Q3 hence the isopivot of K1388.

The tangents at S1, S2, S3 to K1388 concur at X = {3,373} /\ {64,548} which is not on the cubic. It follows that the lines S1T1, S2T2, S3T3 also concur and K1388 is a psK with respect to the triangle S1S2S3.