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X₁₀₈₄¶

CROSSPOINT OF X₂ AND X₅₁₂

Let \(f(a,b,c) = a^{3}(b^{2} - c^{2})^{2}\). Then the line

X₁₀₈₄ (CROSSPOINT OF X₂ AND X₅₁₂) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1084 = CROSSPOINT OF X_2 AND X_512."""

        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,
            complement,
            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_01084(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1084 = CROSSPOINT OF X_2 AND X_512 on reference triangle ABC."""
            X_670 = eval_trilinear_point(model, A, B, C, '1/(a**(3)*(b**(2) - c**(2)))', ID="X_670", classes=["center"])
            X_1084 = complement(model, A, B, C, X_670, ID="X_1084", classes=["selected", "target"])
            X_39 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) + c**(2))', ID="X_39", classes=["center", "incident"])
            X_597 = eval_trilinear_point(model, A, B, C, '(4*a**(2) + b**(2) + c**(2))/a', ID="X_597", classes=["center", "incident"])
            central_line(model, X_39, X_597, 39, 597, incident=True)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            central_line(model, X_2, X_670, 2, 670, incident=True)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_694 = eval_trilinear_point(model, A, B, C, 'a/(a**(4) - b**(2)*c**(2))', ID="X_694", classes=["center", "incident"])
            central_line(model, X_6, X_694, 6, 694, incident=True)
            return promote_point_to_top(model, X_1084)


        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_1084 on the given reference triangle."""
            model = create_model('X_1084 = CROSSPOINT OF X_2 AND X_512')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01084(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-01084.json"))
            write_center_svg(
                model_acute,
                here / "x-01084.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1084¶

X₁₀₈₄¶