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X₆₄₃¶

TRILINEAR MULTIPLIER FOR KIEPERT PARABOLA

X₆₄₃ satisfies the equation X*(incircle) = Kiepert parabola, where * denotes trilinear multiplication, defined by

X₆₄₃ (TRILINEAR MULTIPLIER FOR KIEPERT PARABOLA) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_643 = TRILINEAR MULTIPLIER FOR KIEPERT PARABOLA."""

        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_00643(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_643 = TRILINEAR MULTIPLIER FOR KIEPERT PARABOLA on reference triangle ABC."""
            X_643 = eval_trilinear_point(model, A, B, C, '((b + c - a)/(b**(2) - c**(2)))', ID="X_643", classes=["selected", "target"])
            X_99 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(2) - c**(2))', ID="X_99", classes=["center", "incident"])
            X_109 = eval_trilinear_point(model, A, B, C, 'a/(cos(B) - cos(C))', ID="X_109", classes=["center", "incident"])
            central_line(model, X_99, X_109, 99, 109, incident=True)
            X_100 = eval_trilinear_point(model, A, B, C, '1/(b - c)', ID="X_100", classes=["center", "incident"])
            X_110 = eval_trilinear_point(model, A, B, C, 'csc(B - C)', ID="X_110", classes=["center", "incident"])
            central_line(model, X_100, X_110, 100, 110, incident=True)
            X_162 = eval_trilinear_point(model, A, B, C, '1/(sin(2*B) - sin(2*C))', ID="X_162", classes=["center", "incident"])
            X_190 = eval_trilinear_point(model, A, B, C, 'b*c/(b - c)', ID="X_190", classes=["center", "incident"])
            central_line(model, X_162, X_190, 162, 190, incident=True)
            return promote_point_to_top(model, X_643)


        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_643 on the given reference triangle."""
            model = create_model('X_643 = TRILINEAR MULTIPLIER FOR KIEPERT PARABOLA')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00643(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-00643.json"))
            write_center_svg(
                model_acute,
                here / "x-00643.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X643¶

X₆₄₃¶