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X₃₀₉₈¶

INTERSECTION OF LINES X₃X_6 AND X₆₉X_74

Let AA₁A₂, BB₁B₂, CC₁C₂ be the circumcircle-inscribed equilateral triangles used in the construction of the Trinh triangle. Let A' be the midpoint of A₁ and A₂, and define B' and C' cyclically. Triangle A'B'C' is homothetic to ABC at X₃ and perspective to the Trinh triangle at X₃₀₉₈.

X₃₀₉₈ (INTERSECTION OF LINES X₃X_6 AND X₆₉X_74) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3098 = INTERSECTION OF LINES X_3X_6 AND X_69X_74."""

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


        def construct_x_03098(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3098 = INTERSECTION OF LINES X_3X_6 AND X_69X_74 on reference triangle ABC."""
            X_3098 = eval_trilinear_point(model, A, B, C, 'a*(a**(4) - 2*b**(4) - 2*c**(4) - 2*b**(2)*c**(2) + c**(2)*a**(2) + a**(2)*b**(2))', ID="X_3098", classes=["selected", "target"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            central_line(model, X_3, X_6, 3, 6, incident=True)
            X_69 = eval_trilinear_point(model, A, B, C, '(cos(A))/a**(2)', ID="X_69", classes=["center", "incident"])
            X_74 = eval_trilinear_point(model, A, B, C, '1/(cos(A) - 2*cos(B)*cos(C))', ID="X_74", classes=["center", "incident"])
            central_line(model, X_69, X_74, 69, 74, incident=True)
            X_30 = eval_trilinear_point(model, A, B, C, 'cos(A) - 2*cos(B)*cos(C)', ID="X_30", classes=["center", "incident"])
            X_141 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2) + c**(2))', ID="X_141", classes=["center", "incident"])
            central_line(model, X_30, X_141, 30, 141, incident=True)
            return promote_point_to_top(model, X_3098)


        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_3098 on the given reference triangle."""
            model = create_model('X_3098 = INTERSECTION OF LINES X_3X_6 AND X_69X_74')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03098(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-03098.json"))
            write_center_svg(
                model_acute,
                here / "x-03098.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3098¶

X₃₀₉₈¶