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X₈₁₀¶

CROSSPOINT OF X₁ AND X₁₆₃

X₈₁₀ is the crosspoint of X₁ and X₁₆₃.

X₈₁₀ (CROSSPOINT OF X₁ AND X₁₆₃) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_810 = CROSSPOINT OF X_1 AND X_163."""

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


        def construct_x_00810(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_810 = CROSSPOINT OF X_1 AND X_163 on reference triangle ABC."""
            X_810 = eval_trilinear_point(model, A, B, C, 'sin(2*A)*((cos(B))**(2) - (cos(C))**(2))', ID="X_810", classes=["selected", "target"])
            X_521 = eval_trilinear_point(model, A, B, C, '(sec(B) - sec(C))*(csc(A))', ID="X_521", classes=["center", "incident"])
            X_656 = eval_trilinear_point(model, A, B, C, 'tan(B) - tan(C)', ID="X_656", classes=["center", "incident"])
            central_line(model, X_521, X_656, 521, 656, incident=True)
            X_661 = eval_trilinear_point(model, A, B, C, 'cot(B) - cot(C)', ID="X_661", classes=["center", "incident"])
            X_663 = eval_trilinear_point(model, A, B, C, 'a*(b - c)*(b + c - a)', ID="X_663", classes=["center", "incident"])
            central_line(model, X_661, X_663, 661, 663, incident=True)
            X_667 = eval_trilinear_point(model, A, B, C, 'a**(2)*(b - c)', ID="X_667", classes=["center", "incident"])
            X_788 = eval_trilinear_point(model, A, B, C, 'a**(2)*(b**(3) - c**(3))', ID="X_788", classes=["center", "incident"])
            central_line(model, X_667, X_788, 667, 788, incident=True)
            return promote_point_to_top(model, X_810)


        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_810 on the given reference triangle."""
            model = create_model('X_810 = CROSSPOINT OF X_1 AND X_163')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00810(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-00810.json"))
            write_center_svg(
                model_acute,
                here / "x-00810.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X810¶

X₈₁₀¶