X₂₁₄

X₂-CEVA CONJUGATE OF X₄₄

X₂₁₄ = midpoint of X₁ and X₁₀₀

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

X₂₁₄ (X₂-CEVA CONJUGATE OF X₄₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {1, 100}

• Related Centers: X₁ (INCENTER), X₁₀₀ (ANTICOMPLEMENT OF FEUERBACH POINT)

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

Search Value (6, 9, 13): \(2.146072322216\)

X₂₁₄ lies on the bicevian conic of X₁ and X₂, which is also QA-Co1 (Nine-point Conic) of quadrangle ABCX₁ (see http://www.chrisvantienhoven.nl/other-quadrangle-objects/15-mathematics/quadrangle-objects/artikelen-qa/76-qa-co1.html) (Randy Hutson, July 20, 2016)

▸ Incident Central Lines12 lines

{1, 88}, {2, 80}, {9, 48}, {10, 140}, {11, 442}, {36, 758}, {44, 1017}, {119, 515}, {142, 528}, {535, 908}, {662, 759}, {1015, 1100}

▸ Functional Relations16 relations

• X₂₁₄ = midpoint of X₁ and X₁₀₀

• X₂₁₄ = reflection of X₁₁ in X₁₁₂₅

• X₂₁₄ = isogonal conjugate of X₁₁₆₈

• X₂₁₄ = complement of X₈₀

• X₂₁₄ = X₂-Ceva conjugate of X₄₄

• X₂₁₄ = crosspoint of X₂ and X₃₂₀

• X₂₁₄ = X₂₁-beth conjugate of X₂₄₄

• X₂₁₄ = perspector of circumconic centered at X₄₄

• X₂₁₄ = center of circumconic that is locus of trilinear poles of lines passing through X₄₄

• X₂₁₄ = X₃₆ of X₁-Brocard triangle

• X₂₁₄ = inner-Garcia-to-ABC similarity image of X₁₀

• X₂₁₄ = X₇₆₈₇-of-excentral-triangle

• X₂₁₄ = crosssum of circumcircle intercepts of line PU(55) (line X₁X₅₁₃)

• X₂₁₄ = center of conic {A, B, C,X₁,X₁₀₀}}

• X₂₁₄ = complementary conjugate of X₃₈₁₄

• X₂₁₄ = QA-P₃ (Gergonne-Steiner Point) of quadrangle ABCX₁ (see http://www.chrisvantienhoven.nl/quadrangle-objects/10-mathematics/quadrangle-objects/18-qa-p3.html)