X₃₇₃

CENTROID OF THE PEDAL TRIANGLE OF THE CENTROID

X₃₇₃ is the centroid of the pedal triangle of the centroid.

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

X₃₇₃ (CENTROID OF THE PEDAL TRIANGLE OF THE CENTROID) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {2, 51}, {5, 113}

• Related Centers: X₂ (CENTROID), X₅₁ (CENTROID OF ORTHIC TRIANGLE), X₅ (NINE-POINT CENTER), X₁₁₃ (JERABEK ANTIPODE)

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = 2bc + ac \cos C + ab \cos B\)

Barycentrics: \(h(a,b,c) : h(b,c,a) : h(c,a,b)\), where \(h(a,b,c) = 2abc + ca^{2}\cos C + ba^{2}\cos B\)

Search Value (6, 9, 13): \(1.793121055895\)

▸ Alternate Coordinates1 form

• Trilinears: \(g(a,b,c) : g(b,c,a) : g(c,a,b)\), where \(g(a,b,c) = a(b^{4} + c^{4} - a^{2}b^{2} - a^{2}c^{2} - 6b^{2}c^{2})\)

▸ Linear Combinations1 combination

• X₃₇₃ = \(2\) X₂ + X₅₁

▸ Incident Central Lines7 lines

{2, 51}, {5, 113}, {110, 575}, {181, 748}, {216, 852}, {354, 375}, {597, 2854}

▸ Functional Relations4 relations

• X₃₇₃ = isogonal conjugate of X₁₁₁₆₉

• X₃₇₃ = isotomic conjugate of polar conjugate of X₃₃₈₄₂

• X₃₇₃ = crossdifference of every pair of points on line X₃₅₂X₁₄₉₉

• X₃₇₃ = {X₂,X₅₁}-harmonic conjugate of X₃₉₁₇