X₂₄₂₁

ISOGONAL CONJUGATE OF X₂₃₉₅

X₂₄₂₁ is the isogonal conjugate of X₂₃₉₅.

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

X₂₄₂₁ (ISOGONAL CONJUGATE OF X₂₃₉₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {2, 6}, {110, 351}

• Related Centers: X₂₃₉₅ (GIBERT-SIMSON TRANSFORM OF X₉₈), X₂ (CENTROID), X₆ (SYMMEDIAN POINT), X₁₁₀ (FOCUS OF KIEPERT PARABOLA), X₃₅₁ (CENTER OF THE PARRY CIRCLE)

Trilinears: \((\sin A) (\sin 2B + \sin 2C - 2 (\cot A) (\sin^{2} B + \sin^{2} C))/(\cot B - \cot C) : :\)

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

Search Value (6, 9, 13): \(-2.000547461523\)

▸ Alternate Coordinates1 form

• Trilinears: \(1/f(a,b,c) : 1/f(b,c,a) : 1/f(c,a,b)\), where f(a,b,c) is as given just before X₂₃₉₄

X₂₄₂₁ lies on the cubic K162.

▸ Incident Central Lines8 lines

{2, 6}, {99, 1625}, {110, 351}, {249, 2420}, {250, 2445}, {648, 670}, {691, 2444}, {805, 881}

▸ Functional Relations5 relations

• X₂₄₂₁ = isogonal conjugate of X₂₃₉₅

• X₂₄₂₁ = crosspoint of X_i and X_j for these (i,j): (110, 805), (877, 2396)

• X₂₄₂₁ = crosssum of X_i and X_j for these (i,j): (512, 2491), (523, 804), (878, 2422)

• X₂₄₂₁ = X₉₂-isoconjugate of X₈₇₈

• X₂₄₂₁ = crossdifference of every pair of points on line X₁₁₅X₅₁₂ (the Simson line of X₉₈)