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X₃₂₈₅¶

INTERSECTION OF LINES X₃X_6 AND X₂₁X_45

Let L denote the line through X₁₀ perpendicular to the Euler line. Coefficients for a trilinear equation for L are the trilinears for X₃₂₈₅.

X₃₂₈₅ (INTERSECTION OF LINES X₃X_6 AND X₂₁X_45) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3285 = INTERSECTION OF LINES X_3X_6 AND X_21X_45."""

        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,
            cevapoint,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            point_from_barycentrics,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03285(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3285 = INTERSECTION OF LINES X_3X_6 AND X_21X_45 on reference triangle ABC."""
            X_902 = eval_trilinear_point(model, A, B, C, 'a*(b + c - 2*a)', ID="X_902", classes=["center"])
            X_2251 = point_from_barycentrics(model, A, B, C, -0.57339457, 2.3119275e-07, 1.5733943, ID="X_2251", classes=["center"])
            X_3285 = cevapoint(model, A, B, C, X_902, X_2251, ID="X_3285", classes=["selected", "target"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            central_line(model, X_3, X_6, 3, 6, incident=True)
            X_21 = eval_trilinear_point(model, A, B, C, '1/(cos(B) + cos(C))', ID="X_21", classes=["center", "incident"])
            X_45 = eval_trilinear_point(model, A, B, C, '2*b + 2*c - a', ID="X_45", classes=["center", "incident"])
            central_line(model, X_21, X_45, 21, 45, incident=True)
            X_81 = eval_trilinear_point(model, A, B, C, '1/(b + c)', ID="X_81", classes=["center", "incident"])
            X_89 = eval_trilinear_point(model, A, B, C, '1/(2*b + 2*c - a)', ID="X_89", classes=["center", "incident"])
            central_line(model, X_81, X_89, 81, 89, incident=True)
            return promote_point_to_top(model, X_3285)


        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_3285 on the given reference triangle."""
            model = create_model('X_3285 = INTERSECTION OF LINES X_3X_6 AND X_21X_45')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03285(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-03285.json"))
            write_center_svg(
                model_acute,
                here / "x-03285.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3285¶

X₃₂₈₅¶