X₇₃₃

EVEN (- 2, 2) CIRCUMCIRCLE POINT

X₇₃₃ = trilinear pole of line X₆X₆₈₈

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

X₇₃₃ (EVEN (- 2, 2) CIRCUMCIRCLE POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {39, 83}, {110, 251}

• Related Centers: X₇₃₂ (EVEN (- 2, 2) INFINITY POINT), X₃₉ (BROCARD MIDPOINT), X₈₃ (CEVAPOINT OF CENTROID AND SYMMEDIAN POINT), X₁₁₀ (FOCUS OF KIEPERT PARABOLA), X₂₅₁ (ISOGONAL CONJUGATE OF X₁₄₁)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = 1/[a^{-3}(b^{2} + c^{2}) - a^{1}(b^{-2} + c ^{-2})]\)

Barycentrics: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = af(a,b,c)\)

Search Value (6, 9, 13): \(-0.104982804195\)

X₇₃₃ lies on the circumcircle.

▸ Incident Central Lines7 lines

{2, 689}, {32, 827}, {39, 83}, {100, 893}, {101, 904}, {110, 251}, {755, 882}

▸ Functional Relations5 relations

• X₇₃₃ = isogonal conjugate of X₇₃₂

• X₇₃₃ = isotomic conjugate of X₃₅₅₄₀

• X₇₃₃ = orthoptic-circle-of-Steiner-inellipse-inverse of X₃₅₉₇₁

• X₇₃₃ = trilinear pole of line X₆X₆₈₈

• X₇₃₃ = Ψ(X₆, X₆₈₈)