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X₁₆₂¶

CEVAPOINT OF X₁₀₈ AND X₁₀₉

X₁₆₂ is the cevapoint of X₁₀₈ and X₁₀₉.

X₁₆₂ (CEVAPOINT OF X₁₀₈ AND X₁₀₉) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_162 = CEVAPOINT OF X_108 AND X_109."""

        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_00162(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_162 = CEVAPOINT OF X_108 AND X_109 on reference triangle ABC."""
            X_162 = eval_trilinear_point(model, A, B, C, '1/(sin(2*B) - sin(2*C))', ID="X_162", classes=["selected", "target"])
            X_29 = eval_trilinear_point(model, A, B, C, '(sec(A))/(cos(B) + cos(C))', ID="X_29", classes=["center", "incident"])
            X_58 = eval_trilinear_point(model, A, B, C, 'a/(b + c)', ID="X_58", classes=["center", "incident"])
            central_line(model, X_29, X_58, 29, 58, incident=True)
            X_28 = eval_trilinear_point(model, A, B, C, '(tan(A))/(b + c)', ID="X_28", classes=["center", "incident"])
            X_88 = eval_trilinear_point(model, A, B, C, '1/(b + c - 2*a)', ID="X_88", classes=["center", "incident"])
            central_line(model, X_28, X_88, 28, 88, incident=True)
            X_31 = eval_trilinear_point(model, A, B, C, 'a**(2)', ID="X_31", classes=["center", "incident"])
            X_92 = eval_trilinear_point(model, A, B, C, 'csc(2*A)', ID="X_92", classes=["center", "incident"])
            central_line(model, X_31, X_92, 31, 92, incident=True)
            return promote_point_to_top(model, X_162)


        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_162 on the given reference triangle."""
            model = create_model('X_162 = CEVAPOINT OF X_108 AND X_109')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00162(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-00162.json"))
            write_center_svg(
                model_acute,
                here / "x-00162.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X162¶

X₁₆₂¶