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X₁₁₀₅¶

CEVAPOINT OF X₃ AND X₄

X₁₁₀₅ is the cevapoint of X₃ and X₄.

X₁₁₀₅ (CEVAPOINT OF X₃ AND X₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1105 = CEVAPOINT OF X_3 AND X_4."""

        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_barycentric_point,
            eval_trilinear_point,
            isogonal_conjugate,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01105(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1105 = CEVAPOINT OF X_3 AND X_4 on reference triangle ABC."""
            X_185 = eval_trilinear_point(model, A, B, C, '(cos(A))*(1 - cos(A)*cos(B - C))', ID="X_185", classes=["center"])
            X_1105 = isogonal_conjugate(model, A, B, C, X_185, ID="X_1105", classes=["selected", "target"])
            X_20 = eval_trilinear_point(model, A, B, C, 'cos(A) - cos(B)*cos(C)', ID="X_20", classes=["center", "incident"])
            X_393 = eval_trilinear_point(model, A, B, C, 'b*c*(tan(A))**(2)', ID="X_393", classes=["center", "incident"])
            central_line(model, X_20, X_393, 20, 393, incident=True)
            X_225 = eval_trilinear_point(model, A, B, C, '(sec(A))*(cos(B) + cos(C))', ID="X_225", classes=["center", "incident"])
            X_412 = eval_barycentric_point(model, A, B, C, '(a**(2) + b**(2) - c**(2)) * (a**(2) - b**(2) + c**(2)) * (a**(6) + a**(5)*b - 2*a**(4)*b**(2) - 2*a**(3)*b**(3) + a**(2)*b**(4) + a*b**(5) + a**(5)*c - a**(4)*b*c - a*b**(4)*c + b**(5)*c - 2*a**(4)*c**(2) + 2*a**(2)*b**(2)*c**(2) - 2*a**(3)*c**(3) - 2*b**(3)*c**(3) + a**(2)*c**(4) - a*b*c**(4) + a*c**(5) + b*c**(5))', ID="X_412", classes=["center", "incident"])
            central_line(model, X_225, X_412, 225, 412, incident=True)
            X_243 = eval_trilinear_point(model, A, B, C, '(sec(A))*((cos(A))**(2) - cos(B)*cos(C))', ID="X_243", classes=["center", "incident"])
            X_411 = eval_trilinear_point(model, A, B, C, '(cos(B)*cos(C) - (cos(A) + cos(B) + cos(C))*cos(A))', ID="X_411", classes=["center", "incident"])
            central_line(model, X_243, X_411, 243, 411, incident=True)
            return promote_point_to_top(model, X_1105)


        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_1105 on the given reference triangle."""
            model = create_model('X_1105 = CEVAPOINT OF X_3 AND X_4')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01105(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-01105.json"))
            write_center_svg(
                model_acute,
                here / "x-01105.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1105¶

X₁₁₀₅¶