← etc / Encyclopedia of Triangle Centers

X₁₃₇₀¶

ANTICOMPLEMENT OF X₂₅

X₁₃₇₀ (ANTICOMPLEMENT OF X₂₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1370 = ANTICOMPLEMENT OF X_25."""

        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,
            promote_point_to_top,
            reflection_in_point,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01370(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1370 = ANTICOMPLEMENT OF X_25 on reference triangle ABC."""
            X_25 = eval_trilinear_point(model, A, B, C, 'sin(A)*tan(A)', ID="X_25", classes=["center"])
            X_1368 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2)/(a**(2) - b**(2) + c**(2)) + c**(2)/(a**(2) + b**(2) - c**(2)))', ID="X_1368", classes=["center"])
            X_1370 = reflection_in_point(model, X_25, X_1368, ID="X_1370", 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_66 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(4) + c**(4) - a**(4))', ID="X_66", classes=["center", "incident"])
            X_69 = eval_trilinear_point(model, A, B, C, '(cos(A))/a**(2)', ID="X_69", classes=["center", "incident"])
            central_line(model, X_66, X_69, 66, 69, incident=True)
            X_305 = eval_trilinear_point(model, A, B, C, 'b**(4)*c**(4)*cos(A)', ID="X_305", classes=["center", "incident"])
            X_315 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(4) + c**(4) - a**(4))', ID="X_315", classes=["center", "incident"])
            central_line(model, X_305, X_315, 305, 315, incident=True)
            return promote_point_to_top(model, X_1370)


        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_1370 on the given reference triangle."""
            model = create_model('X_1370 = ANTICOMPLEMENT OF X_25')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01370(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-01370.json"))
            write_center_svg(
                model_acute,
                here / "x-01370.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1370¶

X₁₃₇₀¶