X₂₆₆

ISOGONAL CONJUGATE OF X₁₈₈

X₂₆₆ is the isogonal conjugate of X₁₈₈.

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

X₂₆₆ (ISOGONAL CONJUGATE OF X₁₈₈) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1, 164}, {174, 188}

• Related Centers: X₁₈₈ (2nd MID-ARC POINT OF ANTICOMPLEMENTARY TRIANGLE), X₁ (INCENTER), X₁₆₄ (INCENTER OF EXCENTRAL TRIANGLE), X₁₇₄ (YFF CENTER OF CONGRUENCE)

Trilinears: \(\sin A/2 : \sin B/2 : \sin C/2\)

Barycentrics: \(\sin A \sin A/2 : :\)

Search Value (6, 9, 13): \(0.639005784837\)

▸ Alternate Coordinates5 forms

• Trilinears: \([a/(b + c - a)]^{1/2} : :\)

• Trilinears: \(\sin A \sec A/2 : :\)

• Trilinears: \(\cos A' : :\), where J_aJ_bJ_c is the excentral triangle

• Trilinears: |X₁J_a| : |X₁J_b| : |X₁J_c|, where J_aJ_bJ_c is the excentral triangle

• Trilinears: \(\cos(angle BIC) : \cos(angle CIA) : \cos(angle AIB)\)

▸ Incident Central Lines5 lines

{1, 164}, {56, 289}, {174, 188}, {259, 260}, {361, 978}

▸ Functional Relations12 relations

• X₂₆₆ = isogonal conjugate of X₁₈₈

• X₂₆₆ = eigencenter of cevian triangle of X₁₇₄

• X₂₆₆ = eigencenter of anticevian triangle of X₂₅₉

• X₂₆₆ = X₁₇₄-Ceva conjugate of X₂₅₉

• X₂₆₆ = cevapoint of X₁ and X₃₆₁

• X₂₆₆ = X₆-cross conjugate of X₂₈₉

• X₂₆₆ = crosspoint of X₁ and X₅₀₅

• X₂₆₆ = crosssum of X₁ and X₁₆₄

• X₂₆₆ = SS(A→J_a) of X₃, where J_aJ_bJ_c is the excentral triangle

• X₂₆₆ = trilinear square root of X₅₆

• X₂₆₆ = excentral-to-ABC trilinear image of X₄₀

• X₂₆₆ = intouch-to-ABC trilinear image of X₁

Notes

The trilinear polar of X₂₆₆ passes through X₆₇₂₉. (Randy Hutson, October 15, 2018)