X₂₄₉₂

RADICAL CENTER OF {CIRCUMCIRCLE,NINE-POINT-CIRCLE, MOSES CIRCLE}

X₂₄₉₂ = midpoint of X₂₄₈₅ and X₂₄₈₉

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

X₂₄₉₂ (RADICAL CENTER OF {CIRCUMCIRCLE,NINE-POINT-CIRCLE, MOSES CIRCLE}) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {2485, 2489}

• Related Centers: X₂₄₈₅ (RADICAL CENTER OF {CIRCUMCIRCLE, 1ST LEMOINE CIRCLE, NINE-POINT CIRCLE}), X₂₄₈₉ (RADICAL CENTER OF {CIRCUMCIRCLE, NINE-POINT-CIRCLE, 2ND LEMOINE CIRCLE})

Trilinears: \(a(b^{2} - c^{2})(a^{4} - b^{4} - c^{4} + b^{2}c^{2}) : :\)

Search Value (6, 9, 13): \(-1.670359094832\)

▸ Incident Central Lines7 lines

{6, 526}, {111, 351}, {112, 1576}, {115, 804}, {230, 231}, {512, 2030}, {1989, 2395}

▸ Functional Relations15 relations

• X₂₄₉₂ = midpoint of X₂₄₈₅ and X₂₄₈₉

• X₂₄₉₂ = isogonal conjugate of X₁₇₇₀₈

• X₂₄₉₂ = complement of X₃₅₅₂₂

• X₂₄₉₂ = crosspoint of X_i and X_j for these (i,j): (2, 691), (111, 112)

• X₂₄₉₂ = crosssum of X_i and X_j for these (i,j): (6, 690), (524, 525)

• X₂₄₉₂ = crossdifference of every pair of points on line X₃X₆₇

• X₂₄₉₂ = midpoint of X₈₁₀₅ and X₈₁₀₆

• X₂₄₉₂ = center of circle Moses-Parry circle

• X₂₄₉₂ = intersection of tangents to circumcircle at X₁₁₁ and X₁₁₂, and to nine-point-circle at X₁₁₅ and X₁₅₆₀

• X₂₄₉₂ = pole of line X₂₅X₁₁₁ wrt circumcircle

• X₂₄₉₂ = perspector of hyperbola {{A, B, C,X₄,X₂₃}}

• X₂₄₉₂ = polar conjugate of isotomic conjugate of X₉₅₁₇

• X₂₄₉₂ = pole wrt polar circle of line X₂X₃₃₉

• X₂₄₉₂ = intersection of trilinear polars of X₄ and X₂₃

• X₂₄₉₂ = X₆₃-isoconjugate of X₉₃₅