X₁₇₄₈

MIMOSA TRANSFORM OF X₂₆₄

X₁₇₄₈ = cevapoint of X₁₉ and X₉₂₀

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

X₁₇₄₈ (MIMOSA TRANSFORM OF X₂₆₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {19, 27}, {31, 240}

• Related Centers: X₁₈₂₀ (ISOGONAL CONJUGATE OF MIMOSA TRANSFORM OF X), X₁₉ (CLAWSON POINT), X₂₇ (CEVAPOINT OF ORTHOCENTER AND CLAWSON CENTER), X₃₁ (2nd POWER POINT), X₂₄₀ (-LINE CONJUGATE OF X₄₈)

Trilinears: \(\cot A - \tan A : :\)

Search Value (6, 9, 13): \(2.660185521905\)

▸ Alternate Coordinates3 forms

• Trilinears: \((1 + 2 \cos A)/(1 + \cos A) : :\)

• Trilinears: \(\cot 2A : \cot 2B : \cot 2C\)

• Trilinears: \(\cot A' : :\), where H_aH_bH_c is the orthic triangle

▸ Incident Central Lines9 lines

{19, 27}, {31, 240}, {158, 920}, {162, 1096}, {412, 1158}, {653, 1708}, {1013, 1859}, {1445, 1767}, {1776, 1857}

▸ Functional Relations11 relations

• X₁₇₄₈ = isogonal conjugate of X₁₈₂₀

• X₁₇₄₈ = complement of X₁₈₆₆₄

• X₁₇₄₈ = anticomplement of X₁₈₅₈₈

• X₁₇₄₈ = cevapoint of X₁₉ and X₉₂₀

• X₁₇₄₈ = X_i-cross conjugate of X_j for these (i,j): (563, 1), (2180, 47)

• X₁₇₄₈ = X_i-aleph conjugate of X_j for these (i,j): (4, 1740), (92, 1), (264, 63), (331, 1445), (811, 662), (823, 162), (1969, 1760)

• X₁₇₄₈ = SS(A → H_a) of X₆₃, where H_aH_bH_c is the orthic triangle

• X₁₇₄₈ = {X₁₉,X₆₃}-harmonic conjugate of X₉₂

• X₁₇₄₈ = pole wrt polar circle of trilinear polar of X₉₁ (line X₆₆₁X₂₆₁₈)

• X₁₇₄₈ = polar conjugate of X₉₁

• X₁₇₄₈ = trilinear product X₂*X₂₄