← etc / Encyclopedia of Triangle Centers

X₃₆₂₁¶

H(X₈; M, 2)

X₃₆₂₁ (H(X₈; M, 2)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3621 = H(X_8; M, 2)."""

        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,
            centroid_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            incenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03621(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3621 = H(X_8; M, 2) on reference triangle ABC."""
            X_3621 = eval_trilinear_point(model, A, B, C, 'b*c*(5*a - 3*b - 3*c)', ID="X_3621", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            central_line(model, X_1, X_2, 1, 2, incident=True)
            X_44 = eval_trilinear_point(model, A, B, C, 'b + c - 2*a', ID="X_44", classes=["center", "incident"])
            X_346 = eval_trilinear_point(model, A, B, C, 'b*c*(b + c - a)**(2)', ID="X_346", classes=["center", "incident"])
            central_line(model, X_44, X_346, 44, 346, incident=True)
            X_45 = eval_trilinear_point(model, A, B, C, '2*b + 2*c - a', ID="X_45", classes=["center", "incident"])
            X_391 = eval_trilinear_point(model, A, B, C, 'b*c*(3*a + b + c)*(b + c - a)', ID="X_391", classes=["center", "incident"])
            central_line(model, X_45, X_391, 45, 391, incident=True)
            return promote_point_to_top(model, X_3621)


        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_3621 on the given reference triangle."""
            model = create_model('X_3621 = H(X_8; M, 2)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03621(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-03621.json"))
            write_center_svg(
                model_acute,
                here / "x-03621.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3621¶

X₃₆₂₁¶