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X₃₅₂₂¶

EULER LINE INTERCEPT OF LINE X₈X_165

Other recent results on representations of points on the Euler line are given in

X₃₅₂₂ (EULER LINE INTERCEPT OF LINE X₈X_165) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3522 = EULER LINE INTERCEPT OF LINE X_8X_165."""

        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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            midpoint,
            nagel_point_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03522(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3522 = EULER LINE INTERCEPT OF LINE X_8X_165 on reference triangle ABC."""
            X_20 = eval_trilinear_point(model, A, B, C, 'cos(A) - cos(B)*cos(C)', ID="X_20", classes=["center"])
            X_3091 = eval_trilinear_point(model, A, B, C, 'cos(B)*cos(C) + cos(B - C)', ID="X_3091", classes=["center"])
            X_3522 = midpoint(model, X_20, X_3091, ID="X_3522", classes=["selected", "target"], guide=False)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            central_line(model, X_2, X_3, 2, 3)
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center", "incident"])
            X_165 = eval_trilinear_point(model, A, B, C, 'tan(B/2) + tan(C/2) - tan(A/2)', ID="X_165", classes=["center", "incident"])
            central_line(model, X_8, X_165, 8, 165, incident=True)
            X_40 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C) - cos(A) - 1', ID="X_40", classes=["center", "incident"])
            X_145 = eval_trilinear_point(model, A, B, C, 'b*c*(3*a - b - c)', ID="X_145", classes=["center", "incident"])
            central_line(model, X_40, X_145, 40, 145, incident=True)
            return promote_point_to_top(model, X_3522)


        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_3522 on the given reference triangle."""
            model = create_model('X_3522 = EULER LINE INTERCEPT OF LINE X_8X_165')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03522(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-03522.json"))
            write_center_svg(
                model_acute,
                here / "x-03522.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3522¶

X₃₅₂₂¶