X₃₅₇₇

ISOGONAL CONJUGATE OF X₃₅₇₆

X₃₅₇₇ is the isogonal conjugate of X₃₅₇₆.

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

X₃₅₇₇ (ISOGONAL CONJUGATE OF X₃₅₇₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {21, 40}, {1, 227}

• Related Centers: X₁ (INCENTER), X₂₀₉₃ (REFLECTION OF X₁ IN X₅₇), X₂₁ (SCHIFFLER POINT), X₄₀ (BEVAN POINT), X₂₂₇ (-CEVA CONJUGATE OF X₆₅)

Trilinears: \(1/[(3a - b - c)(a - b + c)(a + b - c) - 4abc] : :\)

Search Value (6, 9, 13): \(-2.343594524012\)

▸ Incident Central Lines18 lines

{1, 227}, {4, 3340}, {7, 515}, {8, 908}, {9, 374}, {21, 40}, {30, 3255}, {80, 1537}, {314, 322}, {943, 1697}, {971, 1159}, {1000, 1512}, {1156, 2800}, {1172, 2331}, {1476, 3333}, {1709, 3065}, {2320, 3306}, {3243, 3254}

▸ Functional Relations4 relations

• X₃₅₇₇ = isogonal conjugate of X₃₅₇₆

• X₃₅₇₇ = cevapoint of X₁ and X₂₀₉₃

• X₃₅₇₇ = X₂₀₉₉-cross conjugate of X₁

• X₃₅₇₇ = trilinear pole of line X₆₅₀X₁₇₆₉

Notes

In the plane of a triangle ABC, let

• A'B'C' = excentral triangle,

• O_a = circle with diameter BC, and define O_b and O_c cyclically;

• P_a = polar of A' with respect to O_a, and define P_b and P_c cyclically;

• A″ = P_c∩P_b, and define B″ and C″ cyclically.

The triangle A″B″C″ is perspective to ABC, and the perspector is X₃₅₇₇. (Dasari Naga Vijay Krishna, July 15, 2021)