X₂₂₁₂

X₂-ISOCONJUGATE OF X₃₄₈

X₂₂₁₂ = X₁₉₁₈-cross conjugate of X₂₁₇₅

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

X₂₂₁₂ (X₂-ISOCONJUGATE OF X₃₄₈) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {9, 33}, {25, 31}

• Related Centers: X₁₉₁₈ (BICENTRIC SUM OF PU(12)), X₂₁₇₅ (-ISOCONJUGATE OF X₈₅), X₉ (MITTENPUNKT), X₃₃ (PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES), X₂₅ (HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES), X₃₁ (2nd POWER POINT)

Trilinears: \(a/f(a,b,c) : b/f(b,c,a) : c/f(c,a,b)\), where f(a,b,c) is as in X₃₄₈

Barycentrics: \(a^{2}/f(a,b,c) : b^{2}/f(b,c,a): c^{2}/f(c,a,b)\)

Search Value (6, 9, 13): \(-13.325031769042\)

▸ Alternate Coordinates1 form

• Trilinears: \(g(A,B,C) : g(B,C,A) : g(C,A,B)\), where \(g(A, B, C) = (\sin A)(\sin A + \tan A)\)

▸ Incident Central Lines18 lines

{4, 238}, {6, 2356}, {9, 33}, {19, 2195}, {24, 601}, {25, 31}, {41, 2204}, {108, 1423}, {171, 459}, {213, 1973}, {427, 748}, {468, 750}, {607, 1253}, {1041, 1445}, {1471, 1876}, {1474, 2279}, {1918, 2207}, {2189, 2311}

▸ Functional Relations4 relations

• X₂₂₁₂ = X_i-Ceva conjugate of X_j for these (i,j): (25, 1973), (33, 41), (2299, 607)

• X₂₂₁₂ = X₁₉₁₈-cross conjugate of X₂₁₇₅

• X₂₂₁₂ = crosspoint of X_i and X_j for these (i,j): (25, 607), (2204, 2299)

• X₂₂₁₂ = crosssum of X_i and X_j for these (i,j): (69, 348), (307, 1231)