X₁₃₃₂

ORTHOCORRESPONDENT OF X₁₀₀

For the definition of orthocorrespondent, see the notes just before X₁₉₉₂.

5, 6, 7 3, 4, 5 Kepler Kimberling

X₁₃₃₂ (ORTHOCORRESPONDENT OF X₁₀₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {2991, 6}

• Related Centers: X₂₉₉₁ (DC(X₁₀₅)), X₆ (SYMMEDIAN POINT)

Trilinears: \((b^{2} + c^{2} - a^{2})/(b - c) : :\)

Search Value (6, 9, 13): \(-39.711519858476\)

▸ Alternate Coordinates1 form

• Trilinears: \((\cot A)/(b - c) : :\)

X₁₃₃₂ lies on the MacBeath circumconic.

▸ Incident Central Lines13 lines

{6, 344}, {69, 219}, {72, 895}, {100, 110}, {101, 1310}, {190, 644}, {287, 336}, {345, 394}, {645, 648}, {646, 1016}, {677, 765}, {815, 932}, {4561, 4574}

▸ Functional Relations9 relations

• X₁₃₃₂ = reflection of X₂₉₉₁ in X₆

• X₁₃₃₂ = isogonal conjugate of X₆₅₉₁

• X₁₃₃₂ = isotomic conjugate of X₁₇₉₂₄

• X₁₃₃₂ = MacBeath circumconic antipode of X₂₉₉₁

• X₁₃₃₂ = trilinear pole of line X₃X₆₃

• X₁₃₃₂ = X₉₂-isoconjugate of X₆₆₇

• X₁₃₃₂ = X_i-Ceva conjugate of X_j for these (i,j): (645, 190), (668, 100), (1016, 345)

• X₁₃₃₂ = X_i-cross conjugate of X_j for these (i,j): (521, 69), (905, 63), (906, 100)

• X₁₃₃₂ = cevapoint of X_i and X_j for these (i,j): (63, 905), (71, 1459), (219, 521)