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X₃₃₄₁¶

X₂-CEVA CONJUGATE OF X₂₈₂

X₃₃₄₁ (X₂-CEVA CONJUGATE OF X₂₈₂) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3341 = X_2-CEVA CONJUGATE OF X_282."""

        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,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            intersect_lines,
            orthocenter_of,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03341(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3341 = X_2-CEVA CONJUGATE OF X_282 on reference triangle ABC."""
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center"])
            X_57 = eval_trilinear_point(model, A, B, C, '1/(b + c - a)', ID="X_57", classes=["center"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_271 = eval_trilinear_point(model, A, B, C, '((cot(A)*cot(A/2))/(-1 - cos(A) + cos(B) + cos(C)))', ID="X_271", classes=["center"])
            central_line(model, X_4, X_57, 4, 57)
            central_line(model, X_2, X_271, 2, 271)
            X_3341 = intersect_lines(model, X_4, X_57, X_2, X_271, ID="X_3341", classes=["selected", "target"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_282 = eval_trilinear_point(model, A, B, C, '(cot(A/2))/(-1 - cos(A) + cos(B) + cos(C))', ID="X_282", classes=["center", "incident"])
            central_line(model, X_6, X_282, 6, 282, incident=True)
            return promote_point_to_top(model, X_3341)


        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_3341 on the given reference triangle."""
            model = create_model('X_3341 = X_2-CEVA CONJUGATE OF X_282')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03341(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-03341.json"))
            write_center_svg(
                model_acute,
                here / "x-03341.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3341¶

X₃₃₄₁¶