← etc / Encyclopedia of Triangle Centers

X₁₃₇¶

X₁₁₀-OF-ORTHIC-TRIANGLE

X₁₃₇ (X₁₁₀-OF-ORTHIC-TRIANGLE) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_137 = X_110-OF-ORTHIC-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,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            nine_point_center_of,
            point_from_barycentrics,
            promote_point_to_top,
            reflection_in_point,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00137(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_137 = X_110-OF-ORTHIC-TRIANGLE on reference triangle ABC."""
            X_128 = eval_trilinear_point(model, A, B, C, '((sec(A))*(cos(2*B) + cos(2*C))*(1 + 2*cos(2*A))*(cos(2*A) + 2*cos(2*B)*cos(2*C)))', ID="X_128", classes=["center"])
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center"])
            X_137 = reflection_in_point(model, X_128, X_5, ID="X_137", classes=["selected", "target"], guide=False)
            central_line(model, X_5, X_128, 5, 128, incident=True)
            X_51 = eval_trilinear_point(model, A, B, C, 'a**(2)*cos(B - C)', ID="X_51", classes=["center", "incident"])
            X_129 = point_from_barycentrics(model, A, B, C, 0.22802261, -0.036048578, 0.80802596, ID="X_129", classes=["center", "incident"])
            central_line(model, X_51, X_129, 51, 129, incident=True)
            X_53 = eval_trilinear_point(model, A, B, C, 'tan(A)*cos(B - C)', ID="X_53", classes=["center", "incident"])
            X_138 = point_from_barycentrics(model, A, B, C, 0.092526257, 0.069481522, 0.83799222, ID="X_138", classes=["center", "incident"])
            central_line(model, X_53, X_138, 53, 138, incident=True)
            return promote_point_to_top(model, X_137)


        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_137 on the given reference triangle."""
            model = create_model('X_137 = X_110-OF-ORTHIC-TRIANGLE')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00137(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-00137.json"))
            write_center_svg(
                model_acute,
                here / "x-00137.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X137¶

X₁₃₇¶