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X₁₅₆¶

X₅-OF-TANGENTIAL-TRIANGLE

X₁₅₆ is the {X₁₅₄,X₁₅₅}-harmonic conjugate of X₂₆. For a list of harmonic conjugates, click Tables at the top of this page.

X₁₅₆ (X₅-OF-TANGENTIAL-TRIANGLE) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_156 = X_5-OF-TANGENTIAL-TRIANGLE."""

        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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            midpoint,
            orthocenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00156(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_156 = X_5-OF-TANGENTIAL-TRIANGLE on reference triangle ABC."""
            X_26 = eval_trilinear_point(model, A, B, C, 'a*(b**(2)*cos(2*B) + c**(2)*cos(2*C) - a**(2)*cos(2*A))', ID="X_26", classes=["center"])
            X_155 = eval_trilinear_point(model, A, B, C, '(cos(A))*((cos(B))**(2) + (cos(C))**(2) - (cos(A))**(2))', ID="X_155", classes=["center"])
            X_156 = midpoint(model, X_26, X_155, ID="X_156", classes=["selected", "target"], guide=False)
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_49 = eval_trilinear_point(model, A, B, C, 'cos(3*A)', ID="X_49", classes=["center", "incident"])
            central_line(model, X_4, X_49, 4, 49, incident=True)
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_74 = eval_trilinear_point(model, A, B, C, '1/(cos(A) - 2*cos(B)*cos(C))', ID="X_74", classes=["center", "incident"])
            central_line(model, X_3, X_74, 3, 74, incident=True)
            X_25 = eval_trilinear_point(model, A, B, C, 'sin(A)*tan(A)', ID="X_25", classes=["center", "incident"])
            X_143 = eval_trilinear_point(model, A, B, C, '(sec(A))*(cos(2*C - 2*A) + cos(2*A - 2*B))', ID="X_143", classes=["center", "incident"])
            central_line(model, X_25, X_143, 25, 143, incident=True)
            return promote_point_to_top(model, X_156)


        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_156 on the given reference triangle."""
            model = create_model('X_156 = X_5-OF-TANGENTIAL-TRIANGLE')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00156(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-00156.json"))
            write_center_svg(
                model_acute,
                here / "x-00156.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X156¶

X₁₅₆¶