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X₂₈₆₇¶

SM(X₁₀₇, X₁₁₀)

X₂₈₆₇ = intersection of antipedal lines of X₁₁₂ and X₁₂₉₇

X₂₈₆₇ (SM(X₁₀₇, X₁₁₀)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2867 = SM(X_107, X_110)."""

        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,
            intersect_lines,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02867(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2867 = SM(X_107, X_110) on reference triangle ABC."""
            X_112 = eval_trilinear_point(model, A, B, C, 'a/(sin(2*B) - sin(2*C))', ID="X_112", classes=["center"])
            X_525 = eval_trilinear_point(model, A, B, C, '(b*cos(B) - c*cos(C))/a', ID="X_525", classes=["center"])
            X_107 = eval_trilinear_point(model, A, B, C, '1/(cos(A)*(sin(2*B) - sin(2*C)))', ID="X_107", classes=["center"])
            X_850 = eval_trilinear_point(model, A, B, C, '(b**(2) - c**(2))/a**(3)', ID="X_850", classes=["center"])
            central_line(model, X_112, X_525, 112, 525)
            central_line(model, X_107, X_850, 107, 850)
            X_2867 = intersect_lines(model, X_112, X_525, X_107, X_850, ID="X_2867", classes=["selected", "target"])
            X_1297 = eval_trilinear_point(model, A, B, C, '(a/(b**(6) + c**(6) - 2*a**(6) + a**(4)*b**(2) + a**(4)*c**(2) - b**(4)*c**(2) - b**(2)*c**(4)))', ID="X_1297", classes=["center", "incident"])
            X_1503 = eval_trilinear_point(model, A, B, C, 'sin(A)*tan(omega)  - 2*cos(B)*cos(C)', ID="X_1503", classes=["center", "incident"])
            central_line(model, X_1297, X_1503, 1297, 1503, incident=True)
            return promote_point_to_top(model, X_2867)


        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_2867 on the given reference triangle."""
            model = create_model('X_2867 = SM(X_107, X_110)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02867(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-02867.json"))
            write_center_svg(
                model_acute,
                here / "x-02867.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2867¶

X₂₈₆₇¶