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X₉₇₁¶

INTERSECTION OF LINES X₃X_9 AND X₄X_7

As the isogonal conjugate of a point on the circumcircle, X₉₇₁ lies on the line at infinity.

X₉₇₁ (INTERSECTION OF LINES X₃X_9 AND X₄X_7) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_971 = INTERSECTION OF LINES X_3X_9 AND X_4X_7."""

        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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            gergonne_point_of,
            mittenpunkt_of,
            orthocenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00971(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_971 = INTERSECTION OF LINES X_3X_9 AND X_4X_7 on reference triangle ABC."""
            X_971 = eval_trilinear_point(model, A, B, C, 'a**(4)*(b + c) - 2*a**(3)*(b**(2) + c**(2) - b*c) + 2*a*(b - c)**(2)*(b**(2) + c**(2) + b*c) - (b - c)**(2)*(b + c)**(3)', ID="X_971", classes=["selected", "target"])
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_7 = gergonne_point_of(model, A, B, C, ID="X_7", classes=["center", "incident"])
            central_line(model, X_4, X_7, 4, 7, incident=True)
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_9 = mittenpunkt_of(model, A, B, C, ID="X_9", classes=["center", "incident"])
            central_line(model, X_3, X_9, 3, 9, incident=True)
            X_20 = eval_trilinear_point(model, A, B, C, 'cos(A) - cos(B)*cos(C)', ID="X_20", classes=["center", "incident"])
            X_72 = eval_trilinear_point(model, A, B, C, '(b + c)*cot(A)', ID="X_72", classes=["center", "incident"])
            central_line(model, X_20, X_72, 20, 72, incident=True)
            return promote_point_to_top(model, X_971)


        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_971 on the given reference triangle."""
            model = create_model('X_971 = INTERSECTION OF LINES X_3X_9 AND X_4X_7')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00971(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-00971.json"))
            write_center_svg(
                model_acute,
                here / "x-00971.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X971¶

X₉₇₁¶