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X₃₀₂₇¶

INCIRCLE-ANTIPODE OF X₃₀₂₃

X₃₀₂₇ is the incircle-antipode of X₃₀₂₃.

X₃₀₂₇ (INCIRCLE-ANTIPODE OF X₃₀₂₃) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3027 = INCIRCLE-ANTIPODE OF X_3023."""

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


        def construct_x_03027(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3027 = INCIRCLE-ANTIPODE OF X_3023 on reference triangle ABC."""
            X_3023 = eval_trilinear_point(model, A, B, C, '(b*c*(b + c - a)*(b - c)**(2)*(a**(2) + b*c)**(2))', ID="X_3023", classes=["center"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center"])
            X_3027 = reflection_in_point(model, X_3023, X_1, ID="X_3027", classes=["selected", "target"], guide=False)
            X_11 = feuerbach_point_of(model, A, B, C, ID="X_11", classes=["center", "incident"])
            X_114 = eval_trilinear_point(model, A, B, C, 'b*c*(b*sec(B +  omega  ) + c*sec(C +  omega  ))', ID="X_114", classes=["center", "incident"])
            central_line(model, X_11, X_114, 11, 114, incident=True)
            X_12 = eval_trilinear_point(model, A, B, C, '1 + cos(B - C)', ID="X_12", classes=["center", "incident"])
            X_115 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2) - c**(2))**(2)', ID="X_115", classes=["center", "incident"])
            central_line(model, X_12, X_115, 12, 115, incident=True)
            X_56 = eval_trilinear_point(model, A, B, C, 'a/(b + c - a)', ID="X_56", classes=["center", "incident"])
            X_99 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(2) - c**(2))', ID="X_99", classes=["center", "incident"])
            central_line(model, X_56, X_99, 56, 99, incident=True)
            return promote_point_to_top(model, X_3027)


        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_3027 on the given reference triangle."""
            model = create_model('X_3027 = INCIRCLE-ANTIPODE OF X_3023')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03027(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-03027.json"))
            write_center_svg(
                model_acute,
                here / "x-03027.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3027¶

X₃₀₂₇¶