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X₁₄₇₁¶

X₁₀₀₁-BETH CONJUGATE OF X₁₀₀₁

Let A₁B₁C₁ and A₂B₂C₂ be the 1st and 2nd Auriga triangles. Let A' be the trilinear product A₁*A₂, and define B', C' cyclically. The lines AA', BB', CC' concur in X₁₄₇₁. (Randy Hutson, March 21, 2019)

X₁₄₇₁ (X₁₀₀₁-BETH CONJUGATE OF X₁₀₀₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1471 = X_1001-BETH CONJUGATE OF X_1001."""

        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,
            gergonne_point_of,
            intersect_lines,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01471(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1471 = X_1001-BETH CONJUGATE OF X_1001 on reference triangle ABC."""
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center"])
            X_41 = eval_trilinear_point(model, A, B, C, 'a**(2)*(b + c - a)', ID="X_41", classes=["center"])
            X_31 = eval_trilinear_point(model, A, B, C, 'a**(2)', ID="X_31", classes=["center"])
            X_57 = eval_trilinear_point(model, A, B, C, '1/(b + c - a)', ID="X_57", classes=["center"])
            central_line(model, X_6, X_41, 6, 41)
            central_line(model, X_31, X_57, 31, 57)
            X_1471 = intersect_lines(model, X_6, X_41, X_31, X_57, ID="X_1471", classes=["selected", "target"])
            X_7 = gergonne_point_of(model, A, B, C, ID="X_7", classes=["center", "incident"])
            X_238 = eval_trilinear_point(model, A, B, C, 'a**(2) - b*c', ID="X_238", classes=["center", "incident"])
            central_line(model, X_7, X_238, 7, 238, incident=True)
            return promote_point_to_top(model, X_1471)


        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_1471 on the given reference triangle."""
            model = create_model('X_1471 = X_1001-BETH CONJUGATE OF X_1001')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01471(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-01471.json"))
            write_center_svg(
                model_acute,
                here / "x-01471.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1471¶

X₁₄₇₁¶