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X₃₂₅₀¶

INTERSECTION OF X₃₇X_513 AND X₁₈₇X_237

X₃₂₅₀ = reflection of X₆₄₉ in X₆₆₅

X₃₂₅₀ (INTERSECTION OF X₃₇X_513 AND X₁₈₇X_237) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3250 = INTERSECTION OF X_37X_513 AND X_187X_237."""

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


        def construct_x_03250(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3250 = INTERSECTION OF X_37X_513 AND X_187X_237 on reference triangle ABC."""
            X_649 = eval_trilinear_point(model, A, B, C, 'a*(b - c)', ID="X_649", classes=["center"])
            X_665 = eval_trilinear_point(model, A, B, C, 'a*((a - b)**(2)*(a + b - c) - (c - a)**(2)*(c + a - b))', ID="X_665", classes=["center"])
            X_3250 = reflection_in_point(model, X_649, X_665, ID="X_3250", classes=["selected", "target"], guide=False)
            X_187 = eval_trilinear_point(model, A, B, C, 'a*(2*a**(2) - b**(2) - c**(2))', ID="X_187", classes=["center", "incident"])
            X_237 = eval_trilinear_point(model, A, B, C, 'a**(2)*cos(A +  omega  )', ID="X_237", classes=["center", "incident"])
            central_line(model, X_187, X_237, 187, 237, incident=True)
            X_37 = eval_trilinear_point(model, A, B, C, 'b + c', ID="X_37", classes=["center", "incident"])
            X_513 = eval_trilinear_point(model, A, B, C, 'b - c', ID="X_513", classes=["center", "incident"])
            central_line(model, X_37, X_513, 37, 513, incident=True)
            X_514 = eval_trilinear_point(model, A, B, C, '(b - c)/a', ID="X_514", classes=["center", "incident"])
            X_661 = eval_trilinear_point(model, A, B, C, 'cot(B) - cot(C)', ID="X_661", classes=["center", "incident"])
            central_line(model, X_514, X_661, 514, 661, incident=True)
            return promote_point_to_top(model, X_3250)


        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_3250 on the given reference triangle."""
            model = create_model('X_3250 = INTERSECTION OF X_37X_513 AND X_187X_237')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03250(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-03250.json"))
            write_center_svg(
                model_acute,
                here / "x-03250.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3250¶

X₃₂₅₀¶