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X₁₈₂¶

MIDPOINT OF BROCARD DIAMETER

X₁₈₂ is the midpoint of the Brocard diameter (the segment X₃-to-X₆); also the center of the 1st Lemoine circle, and the center of the Brocard circle.

X₁₈₂ (MIDPOINT OF BROCARD DIAMETER) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_182 = MIDPOINT OF BROCARD DIAMETER."""

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


        def construct_x_00182(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_182 = MIDPOINT OF BROCARD DIAMETER on reference triangle ABC."""
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center"])
            X_182 = midpoint(model, X_3, X_6, ID="X_182", classes=["selected", "target"], guide=False)
            central_line(model, X_3, X_6, 3, 6, incident=True)
            X_22 = eval_trilinear_point(model, A, B, C, 'a*(b**(4) + c**(4) - a**(4))', ID="X_22", classes=["center", "incident"])
            X_51 = eval_trilinear_point(model, A, B, C, 'a**(2)*cos(B - C)', ID="X_51", classes=["center", "incident"])
            central_line(model, X_22, X_51, 22, 51, incident=True)
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_83 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(2) + c**(2))', ID="X_83", classes=["center", "incident"])
            central_line(model, X_4, X_83, 4, 83, incident=True)
            return promote_point_to_top(model, X_182)


        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_182 on the given reference triangle."""
            model = create_model('X_182 = MIDPOINT OF BROCARD DIAMETER')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00182(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-00182.json"))
            write_center_svg(
                model_acute,
                here / "x-00182.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X182¶

X₁₈₂¶