X₁₃₆₄

BRISSE TRANSFORM OF X₁₀₈

X₁₃₆₄ = reflection of X₁₃₆₁ in X₁

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

X₁₃₆₄ (BRISSE TRANSFORM OF X₁₀₈) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1361, 1}

• Related Centers: X₁₃₆₁ (BRISSE TRANSFORM OF X₁₀₄), X₁ (INCENTER)

Trilinears: \(\csc A \tan(A/2) / (\sec B - \sec C) : :\)

Search Value (6, 9, 13): \(3.199467879717\)

▸ Alternate Coordinates1 form

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

X₁₃₆₄ lies on the incircle.

▸ Incident Central Lines11 lines

{1, 1361}, {11, 124}, {12, 117}, {55, 103}, {56, 102}, {65, 1359}, {77, 296}, {151, 388}, {185, 603}, {354, 1360}, {942, 1354}

▸ Functional Relations12 relations

• X₁₃₆₄ = reflection of X₁₃₆₁ in X₁

• X₁₃₆₄ = anticomplement of X₃₀₄₂

• X₁₃₆₄ = X_i-Ceva conjugate of X_j for these (i,j): (7, 905), (189, 650), (222, 652), (255, 520)

• X₁₃₆₄ = crosspoint of X_i and X_j for these (i,j): (3, 521), (7, 905)

• X₁₃₆₄ = crosssum of X₄ and X₁₀₈

• X₁₃₆₄ = X₉₂₅-of-intouch-triangle

• X₁₃₆₄ = X₁₀₉-of-Mandart-incircle-triangle

• X₁₃₆₄ = homothetic center of intangents triangle and reflection of extangents triangle in X₁₀₉

• X₁₃₆₄ = trilinear pole wrt intouch triangle of line X₄X₇

• X₁₃₆₄ = intersection, other than X₁₁, of incircle and Mandart circle

• X₁₃₆₄ = extouch isogonal conjugate of X₅₂₂

• X₁₃₆₄ = crossdifference of every pair of points on line X₁₇₈₃X₄₅₅₉