X₃₀₆₄

ISOGONAL CONJUGATE OF X₁₈₁₃

X₃₀₆₄ is the isogonal conjugate of X₁₈₁₃.

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

X₃₀₆₄ (ISOGONAL CONJUGATE OF X₁₈₁₃) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {230, 231}, {19, 649}

• Related Centers: X₁₈₁₃ (INVERSE MIMOSA TRANSFORM OF X₆₅₀), X₂₃₀ (-CEVA CONJUGATE OF X₁₁₄), X₂₃₁ (-CEVA CONJUGATE OF X₁₂₈), X₁₉ (CLAWSON POINT), X₆₄₉ (CROSSDIFFERENCE OF X₁ and X₂)

Trilinears: \((\cos B - \cos C)/\cos A : (\cos C - \cos A)/\cos B : (\cos A - \cos B)/\cos C\)

Barycentrics: \((\cos B - \cos C) \tan A : (\cos C - \cos A) \tan B : (\cos A - \cos B) \tan C\)

Search Value (6, 9, 13): \(-6.194435503824\)

X₃₀₆₄ lies on radical axis of Mandart circle and excircles radical circle. (Randy Hutson, December 2, 2017)

▸ Incident Central Lines5 lines

{19, 649}, {112, 2689}, {225, 770}, {230, 231}, {243, 522}

▸ Functional Relations12 relations

• X₃₀₆₄ = isogonal conjugate of X₁₈₁₃

• X₃₀₆₄ = X_i-Ceva conjugate of X_j for these (i,j): (108, 1856), (158, 2310), (278, 11), (653, 4), (1783, 1826), (1897, 33)

• X₃₀₆₄ = cevapoint of X₆₆₁ and X₂₅₀₁

• X₃₀₆₄ = X_i-cross conjugate of X_j for these (i,j): (661, 650), (663, 522), (2170, 19), (2310, 158)

• X₃₀₆₄ = crosspoint of X_i and X_j for these (i,j): (4, 653), (92, 1897), (1172, 1783)

• X₃₀₆₄ = crosssum of X_i and X_j for these (i,j): (3, 652), (48, 1459), 905,1214)

• X₃₀₆₄ = crossdifference of every pair of points on the line X₃X₇₃

• X₃₀₆₄ = pole wrt polar circle of trilinear polar of X₆₆₄ (line X₂X₇)

• X₃₀₆₄ = polar conjugate of X₆₆₄

• X₃₀₆₄ = trilinear pole of line X₂₃₁₀X₈₇₃₅

• X₃₀₆₄ = trilinear product X₄*X₆₅₀

• X₃₀₆₄ = trilinear product of Feuerbach hyperbola intercepts of orthic axis