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X₁₄₇¶

TARRY POINT OF ANTICOMPLEMENTARY TRIANGLE

X₁₄₇ is the {X₉₈,X₁₁₄}-harmonic conjugate of X₂. For a list of harmonic conjugates, click Tables at the top of this page.

X₁₄₇ (TARRY POINT OF ANTICOMPLEMENTARY TRIANGLE) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_147 = TARRY POINT OF ANTICOMPLEMENTARY TRIANGLE."""

        from __future__ import annotations

        from pathlib import Path

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

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


        def construct_x_00147(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_147 = TARRY POINT OF ANTICOMPLEMENTARY TRIANGLE on reference triangle ABC."""
            X_98 = eval_trilinear_point(model, A, B, C, 'sec(A +  omega  )', ID="X_98", classes=["center"])
            X_147 = anticomplement(model, A, B, C, X_98, ID="X_147", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            central_line(model, X_2, X_98, 2, 98, incident=True)
            X_20 = eval_trilinear_point(model, A, B, C, 'cos(A) - cos(B)*cos(C)', ID="X_20", classes=["center", "incident"])
            X_99 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(2) - c**(2))', ID="X_99", classes=["center", "incident"])
            central_line(model, X_20, X_99, 20, 99, incident=True)
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_150 = eval_trilinear_point(model, A, B, C, '(b*c*(b**(4) + c**(4) - a**(4) + a*(b*c**(2) +c*b**(2) - b**(3) - c**(3)) - b*c*(a**(2) + b**(2) + c**(2)) + (b + c)*a**(3)))', ID="X_150", classes=["center", "incident"])
            central_line(model, X_1, X_150, 1, 150, incident=True)
            return promote_point_to_top(model, X_147)


        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_147 on the given reference triangle."""
            model = create_model('X_147 = TARRY POINT OF ANTICOMPLEMENTARY TRIANGLE')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00147(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-00147.json"))
            write_center_svg(
                model_acute,
                here / "x-00147.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X147¶

X₁₄₇¶