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X₃₃₈¶

CEVAPOINT OF X₁₁₅ AND X₁₂₅

X₃₃₈ is the cevapoint of X₁₁₅ and X₁₂₅.

X₃₃₈ (CEVAPOINT OF X₁₁₅ AND X₁₂₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_338 = CEVAPOINT OF X_115 AND X_125."""

        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,
            isotomic_conjugate,
            orthocenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00338(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_338 = CEVAPOINT OF X_115 AND X_125 on reference triangle ABC."""
            X_249 = eval_trilinear_point(model, A, B, C, '(csc(A))*(csc(B - C))**(2)', ID="X_249", classes=["center"])
            X_338 = isotomic_conjugate(model, A, B, C, X_249, ID="X_338", classes=["selected", "target"])
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_67 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(4) + c**(4) - a**(4) - b**(2)*c**(2))', ID="X_67", classes=["center", "incident"])
            central_line(model, X_4, X_67, 4, 67, incident=True)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_94 = eval_trilinear_point(model, A, B, C, 'csc(3*A)', ID="X_94", classes=["center", "incident"])
            central_line(model, X_2, X_94, 2, 94, incident=True)
            X_115 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2) - c**(2))**(2)', ID="X_115", classes=["center", "incident"])
            X_127 = eval_trilinear_point(model, A, B, C, 'b*c*(sin(2*B) - sin(2*C))*((b**(2) - c**(2))*sin(2*A) - b**(2)*sin(2*B) + c**(2)*sin(2*C))', ID="X_127", classes=["center", "incident"])
            central_line(model, X_115, X_127, 115, 127, incident=True)
            return promote_point_to_top(model, X_338)


        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_338 on the given reference triangle."""
            model = create_model('X_338 = CEVAPOINT OF X_115 AND X_125')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00338(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-00338.json"))
            write_center_svg(
                model_acute,
                here / "x-00338.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X338¶

X₃₃₈¶