X₃₂₇₄

PERSPECTOR OF TRIANGLES P1P2P3 AND J1J2J3

X₃₂₇₄ is the perspector of triangles p1p2p3 and j1j2j3.

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

X₃₂₇₄ (PERSPECTOR OF TRIANGLES P1P2P3 AND J1J2J3) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {16, 358}, {1134, 1136}

• Related Centers: X₃₆₀₂ (ISOGONAL CONJUGATE OF X₃₂₇₄), X₁₆ (2nd ISODYNAMIC POINT), X₃₅₈ (2nd MORLEY-TAYLOR-MARR CENTER), X₁₁₃₄ (3rd MORLEY-TAYLOR-MARR CENTER), X₁₁₃₆ (5th MORLEY-TAYLOR-MARR CENTER)

Trilinears: \(\cos(A/3 + \pi /6) : :\)

Search Value (6, 9, 13): \(2.346473628288\)

▸ Alternate Coordinates1 form

• Trilinears: \(\sin(A/3 - \pi /3) : :\)

▸ Incident Central Lines3 lines

{16, 358}, {1134, 1136}, {3272, 3276}

▸ Functional Relations5 relations

• X₃₂₇₄ = isogonal conjugate of X₃₆₀₂

• X₃₂₇₄ = crosssum of X₃₅₈ and X₃₂₇₅

• X₃₂₇₄ = crossdifference of every pair of points on the perspectrix of ABC and 1st Morley triangle

• X₃₂₇₄ = perspector of ABC and unary cofactor triangle of 1st Morley triangle

• X₃₂₇₄ = perspector of ABC and unary cofactor triangle of 1st Morley adjunct triangle

Notes

Let A'B'C' be the 1st Morley triangle. Let L_a be the trilinear polar of A', and define L_b, L_c cyclically. Let A″ = L_b∩L_c, B″ = L_c∩L_a, C″ = L_a∩L_b. The lines AA″, BB″, CC″ concur in X₃₂₇₄. (Randy Hutson, July 20, 2016)