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X₃₈₆₇¶

PERSPECTOR OF ABC AND T(a², a² + c²)

X₃₈₆₇ is the perspector of ABC and t(a², a² + c²).

X₃₈₆₇ (PERSPECTOR OF ABC AND T(a², a² + c²)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3867 = PERSPECTOR OF ABC AND T(a², a² + c²)."""

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


        def construct_x_03867(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3867 = PERSPECTOR OF ABC AND T(a², a² + c²) on reference triangle ABC."""
            X_3867 = eval_barycentric_point(model, A, B, C, '((b**(2) + c**(2))*(a**(2) + b**(2) - c**(2))*(a**(2) - b**(2) + c**(2))/(3*a**(2) + b**(2) + c**(2)))', ID="X_3867", classes=["selected", "target"])
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            central_line(model, X_4, X_6, 4, 6, incident=True)
            X_141 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2) + c**(2))', ID="X_141", classes=["center", "incident"])
            X_427 = eval_trilinear_point(model, A, B, C, 'sec(A) + cos(B - C)', ID="X_427", classes=["center", "incident"])
            central_line(model, X_141, X_427, 141, 427, incident=True)
            X_428 = eval_trilinear_point(model, A, B, C, '3*sec(A) - csc(A)*tan(omega) ', ID="X_428", classes=["center", "incident"])
            X_597 = eval_trilinear_point(model, A, B, C, '(4*a**(2) + b**(2) + c**(2))/a', ID="X_597", classes=["center", "incident"])
            central_line(model, X_428, X_597, 428, 597, incident=True)
            return promote_point_to_top(model, X_3867)


        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_3867 on the given reference triangle."""
            model = create_model('X_3867 = PERSPECTOR OF ABC AND T(a², a² + c²)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03867(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-03867.json"))
            write_center_svg(
                model_acute,
                here / "x-03867.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3867¶

X₃₈₆₇¶