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too complicated to be written here. Click on the link to download a text file. |
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X(1), X(3), X(4), X(631), X(3338), X(3527), X(7162) excenters other points described below |
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K832 is a member of the Euler pencil. See Table 27. Its pivot X(631) is the harmonic conjugate of H with respect to G and O. The isopivot is X(3527), the "last" point on the Jerabek hyperbola. The polar conic of O is the Jerabek hyperbola JT of the Thomson triangle Q1Q2Q3 hence K832 and JT meet at six points namely O (twice) and P0, P1, P2, P3. The tangents at these points concur at O. The vertices R1, R2, R3 of the diagonal triangle also lie on K832. It follows that K832 is a pK with pivot O with respect to R1R2R3 and P0, P1, P2, P3 are the fixed points of the corresponding isoconjugation. The three points ORi /\ RjRk lie on K832. The Stuyvaert point X(14924) of K832 lies on JT. Recall that it is the only point whose polar conic is a circle. See also Table 47. Peter Moses notes that this point lies on the lines {373,5646}, {392,3646}, {575,3167}, {576,5544}, {1201,2334}, {1350,5888}, {1656,5655}, {1995,6030}, {3090,5656}, {3628,5654}, {5085,7712}. |