← etc / Encyclopedia of Triangle Centers

X₁₁₅₀¶

INTERSECTION OF LINES X₂X_6 AND X₃X_8

X₁₁₅₀ = complement of X₃₁₀₃₄

X₁₁₅₀ (INTERSECTION OF LINES X₂X_6 AND X₃X_8) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1150 = INTERSECTION OF LINES X_2X_6 AND X_3X_8."""

        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,
            nagel_point_of,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01150(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1150 = INTERSECTION OF LINES X_2X_6 AND X_3X_8 on reference triangle ABC."""
            X_1150 = eval_trilinear_point(model, A, B, C, '((b**(2) + c**(2) - a**(2)) + b*c*(b + c)/a)', ID="X_1150", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            central_line(model, X_2, X_6, 2, 6, incident=True)
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center", "incident"])
            central_line(model, X_3, X_8, 3, 8, incident=True)
            X_63 = eval_trilinear_point(model, A, B, C, 'cot(A)', ID="X_63", classes=["center", "incident"])
            X_321 = eval_trilinear_point(model, A, B, C, '(b + c)*b**(2)*c**(2)', ID="X_321", classes=["center", "incident"])
            central_line(model, X_63, X_321, 63, 321, incident=True)
            return promote_point_to_top(model, X_1150)


        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_1150 on the given reference triangle."""
            model = create_model('X_1150 = INTERSECTION OF LINES X_2X_6 AND X_3X_8')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01150(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-01150.json"))
            write_center_svg(
                model_acute,
                here / "x-01150.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1150¶

X₁₁₅₀¶