X₂₁₀

X₁₀-CEVA CONJUGATE OF X₃₇

X₂₁₀ = X₁₀-Ceva conjugate of X₃₇

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

X₂₁₀ (X₁₀-CEVA CONJUGATE OF X₃₇) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {10, 12}, {9, 55}

• Related Centers: X₁₀ (SPIEKER CENTER), X₃₇ (CROSSPOINT OF INCENTER AND CENTROID), X₁₂ ({X), X₉ (MITTENPUNKT), X₅₅ (INSIMILICENTER)

Trilinears: \((b + c)(b + c - a) : (c + a)(c + a - b) : (a + b)(a + b - c)\)

Barycentrics: \(a(b + c)(b + c - a) : b(c + a)(c + a - b) : c(a + b)(a + b - c) : :\)

Search Value (6, 9, 13): \(3.955289807504\)

▸ Alternate Coordinates1 form

• Trilinears: \((\cos B - \cos C)^{2} + (\cos A + 1)(\cos B + \cos C - 2) : :\)

▸ Incident Central Lines25 lines

{1, 2334}, {2, 354}, {6, 612}, {8, 312}, {9, 55}, {10, 12}, {31, 44}, {33, 220}, {37, 42}, {38, 899}, {43, 984}, {45, 968}, {51, 374}, {56, 936}, {63, 1004}, {78, 958}, {165, 971}, {201, 227}, {213, 762}, {381, 517}, {392, 519}, {430, 594}, {869, 1107}, {956, 997}, {976, 1104}

▸ Functional Relations16 relations

• X₂₁₀ = X₂-of-extouch triangle, so that X₂₁₀X₁₁₅₈ = Euler line of the extouch triangle

• X₂₁₀ = reflection of X_i in X_j for these (i,j): (51, 375), (354, 2)

• X₂₁₀ = isogonal conjugate of X₁₀₁₄

• X₂₁₀ = complement of X₃₈₇₃

• X₂₁₀ = anticomplement of X₃₇₄₂

• X₂₁₀ = X₁₀-Ceva conjugate of X₃₇

• X₂₁₀ = crosspoint of X₈ and X₉

• X₂₁₀ = crosssum of X_i and X_j for these (i,j): (56, 57), (58, 1412)

• X₂₁₀ = crossdifference of every pair of points on line X₁₀₁₉X₁₄₂₉

• X₂₁₀ = X_i-beth conjugate of X_j for these (i,j): (200, 210), (210, 42)

• X₂₁₀ = centroid of Bevan circle intercepts with sidelines of ABC

• X₂₁₀ = centroid of AbAcBcBaCaCb as defined at X₃₅₈₈

• X₂₁₀ = centroid of AbAcBcBaCaCb as used in the construction of the inner-Conway triangle; see preamble before X₁₁₆₇₇

• X₂₁₀ = trilinear pole of line X₃₇₀₉X₄₀₄₁

• X₂₁₀ = excentral-to-ABC barycentric image of X₂

• X₂₁₀ = {X₃₇,X₄₂}-harmonic conjugate of X₃₇₅₉₃