X₁₅₉₆

POINT CHELEB II

X₁₅₉₆ = midpoint of X₄ and X₂₅

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

X₁₅₉₆ (POINT CHELEB II) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {4, 25}, {2, 3} (Euler line)

• Related Centers: X₄ (ORTHOCENTER), X₂₅ (HOMOTHETIC CENTER OF ORTHIC AND TANGENTIAL TRIANGLES), X₂ (CENTROID), X₃ (CIRCUMCENTER)

Trilinears: \(2 \sec A - \cos(B - C) : :\)

Search Value (6, 9, 13): \(-3.111512073946\)

▸ Incident Central Lines4 lines

{2, 3}, {33, 495}, {34, 496}, {53, 115}

▸ Functional Relations12 relations

• X₁₅₉₆ = midpoint of X₄ and X₂₅

• X₁₅₉₆ = reflection of X₁₃₆₈ in X₅

• X₁₅₉₆ = circumcircle-inverse of X₃₇₉₃₃

• X₁₅₉₆ = nine-point-circle-inverse of X₃₇₉₈₄

• X₁₅₉₆ = orthocentroidal-circle-inverse of X₁₅₉₇

• X₁₅₉₆ = complementary conjugate of complement of X₃₅₅₁₂

• X₁₅₉₆ = {X₄,X₅}-harmonic conjugate of X₁₅₉₅

• X₁₅₉₆ = X₉₉₉-of-orthic-triangle if ABC is acute

• X₁₅₉₆ = center of inverse-in-polar-circle-of-de-Longchamps-line

• X₁₅₉₆ = polar conjugate of isotomic conjugate of X₃₇₆₄₈

• X₁₅₉₆ = homothetic center of Ehrmann mid-triangle and 3rd pedal triangle of X₄

• X₁₅₉₆ = Ehrmann-side-to-orthic similarity image of X₁₈₅₃₁

Notes

As a point on the Euler line, X₁₅₉₆ has Shinagawa coefficients \((F, -2E + F)\).