← etc / Encyclopedia of Triangle Centers

X₃₇₇₈¶

X₁₉₆₄com[INVERSE(nT(-bc, b²))]

X₃₇₇₈ = isogonal conjugate of isotomic conjugate of X₂₈₈₇

X₃₇₇₈ (X₁₉₆₄com[INVERSE(nT(-bc, b²))]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3778 = X_1964com[INVERSE(nT(-bc, b²))]."""

        from __future__ import annotations

        from pathlib import Path

        import sympy.geometry as spg
        from geometor.model import Model

        from geometor.etc.ops import (
            central_line,
            construct_baseline_triangle,
            create_model,
            eval_barycentric_point,
            eval_trilinear_point,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03778(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3778 = X_1964com[INVERSE(nT(-bc, b²))] on reference triangle ABC."""
            X_3778 = eval_barycentric_point(model, A, B, C, '(a**(2)*(b + c)*(b**(2) + c**(2) - b*c))', ID="X_3778", classes=["selected", "target"])
            X_42 = eval_trilinear_point(model, A, B, C, 'a*(b + c)', ID="X_42", classes=["center", "incident"])
            X_181 = eval_trilinear_point(model, A, B, C, 'a*(b + c)**(2)/(b + c - a)', ID="X_181", classes=["center", "incident"])
            central_line(model, X_42, X_181, 42, 181, incident=True)
            X_142 = eval_trilinear_point(model, A, B, C, 'b + c - ((b - c)**(2))/a', ID="X_142", classes=["center", "incident"])
            X_244 = eval_trilinear_point(model, A, B, C, '(b - c)**(2)', ID="X_244", classes=["center", "incident"])
            central_line(model, X_142, X_244, 142, 244, incident=True)
            X_256 = eval_trilinear_point(model, A, B, C, '1/(a**(2) + b*c)', ID="X_256", classes=["center", "incident"])
            X_291 = eval_trilinear_point(model, A, B, C, '1/(a**(2) - b*c)', ID="X_291", classes=["center", "incident"])
            central_line(model, X_256, X_291, 256, 291, incident=True)
            return promote_point_to_top(model, X_3778)


        def build_model(
            sides: tuple[float, float, float] = (5.0, 6.0, 7.0),
            show_guides: bool = False,
        ) -> Model:
            """Build a `geometor.model.Model` for X_3778 on the given reference triangle."""
            model = create_model('X_3778 = X_1964com[INVERSE(nT(-bc, b²))]')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03778(model, A, B, C)
            return model


        if __name__ == "__main__":
            here = Path(__file__).resolve().parent
            model_acute = build_model((5.0, 6.0, 7.0))
            model_acute.save(str(here / "x-03778.json"))
            write_center_svg(
                model_acute,
                here / "x-03778.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3778¶

X₃₇₇₈¶