← etc / Encyclopedia of Triangle Centers

X₁₀₈₉¶

TRILINEAR SQUARE OF X₁₀

X₁₀₈₉ (TRILINEAR SQUARE OF X₁₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1089 = TRILINEAR SQUARE OF X_10."""

        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,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            incenter_of,
            isogonal_conjugate,
            nagel_point_of,
            promote_point_to_top,
            spieker_center_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01089(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1089 = TRILINEAR SQUARE OF X_10 on reference triangle ABC."""
            X_849 = eval_trilinear_point(model, A, B, C, '(a/(b + c))**(2)', ID="X_849", classes=["center"])
            X_1089 = isogonal_conjugate(model, A, B, C, X_849, ID="X_1089", classes=["selected", "target"])
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center", "incident"])
            X_80 = eval_trilinear_point(model, A, B, C, '1/(1 - 2*cos(A))', ID="X_80", classes=["center", "incident"])
            central_line(model, X_8, X_80, 8, 80, incident=True)
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_312 = eval_trilinear_point(model, A, B, C, '(b + c - a)*b**(2)*c**(2)', ID="X_312", classes=["center", "incident"])
            central_line(model, X_1, X_312, 1, 312, incident=True)
            X_10 = spieker_center_of(model, A, B, C, ID="X_10", 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_10, X_321, 10, 321, incident=True)
            return promote_point_to_top(model, X_1089)


        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_1089 on the given reference triangle."""
            model = create_model('X_1089 = TRILINEAR SQUARE OF X_10')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01089(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-01089.json"))
            write_center_svg(
                model_acute,
                here / "x-01089.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1089¶

X₁₀₈₉¶