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X₃₄₆₂¶

X₅-CEVA CONJUGATE OF X₄

X₃₄₆₂ (X₅-CEVA CONJUGATE OF X₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3462 = X_5-CEVA CONJUGATE OF 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,
            centroid_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            intersect_lines,
            orthocenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03462(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3462 = X_5-CEVA CONJUGATE OF X_4 on reference triangle ABC."""
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center"])
            X_54 = eval_trilinear_point(model, A, B, C, 'sec(B - C)', ID="X_54", classes=["center"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_1075 = eval_trilinear_point(model, A, B, C, '(sec(A))*((sec(B))**(2) + (sec(C))**(2) - (sec(A))**(2))', ID="X_1075", classes=["center"])
            central_line(model, X_4, X_54, 4, 54)
            central_line(model, X_2, X_1075, 2, 1075)
            X_3462 = intersect_lines(model, X_4, X_54, X_2, X_1075, ID="X_3462", classes=["selected", "target"])
            X_233 = eval_trilinear_point(model, A, B, C, '(b*cos(C - A) + c*cos(B - A))*cos(B - C)', ID="X_233", classes=["center", "incident"])
            X_1249 = eval_trilinear_point(model, A, B, C, '(tan(A))*(cos(A) - cos(B)*cos(C))', ID="X_1249", classes=["center", "incident"])
            central_line(model, X_233, X_1249, 233, 1249, incident=True)
            return promote_point_to_top(model, X_3462)


        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_3462 on the given reference triangle."""
            model = create_model('X_3462 = X_5-CEVA CONJUGATE OF X_4')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03462(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-03462.json"))
            write_center_svg(
                model_acute,
                here / "x-03462.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3462¶

X₃₄₆₂¶