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X₃₄₉₁¶

INTERSECTION OF LINES X₁X_295 AND X₄X_69

X₃₄₉₁ (INTERSECTION OF LINES X₁X_295 AND X₄X_69) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3491 = INTERSECTION OF LINES X_1X_295 AND X_4X_69."""

        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,
            ceva_conjugate,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            incenter_of,
            orthocenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03491(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3491 = INTERSECTION OF LINES X_1X_295 AND X_4X_69 on reference triangle ABC."""
            X_384 = eval_trilinear_point(model, A, B, C, 'b*c*(a**(4) + b**(2)*c**(2))', ID="X_384", classes=["center"])
            X_39 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) + c**(2))', ID="X_39", classes=["center"])
            X_3491 = ceva_conjugate(model, A, B, C, X_384, X_39, ID="X_3491", classes=["selected", "target"])
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_69 = eval_trilinear_point(model, A, B, C, '(cos(A))/a**(2)', ID="X_69", classes=["center", "incident"])
            central_line(model, X_4, X_69, 4, 69, incident=True)
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_295 = eval_trilinear_point(model, A, B, C, '(cos(A))/(a**(2) - b*c)', ID="X_295", classes=["center", "incident"])
            central_line(model, X_1, X_295, 1, 295, incident=True)
            X_147 = eval_trilinear_point(model, A, B, C, 'b*c*(a**(8) + (b**(2) + c**(2))*a**(6) - (2*b**(4) + 3*b**(2)*c**(2) + 2*c**(4))*a**(4) + (b**(6) + b**(4)*c**(2) + b**(2)*c**(4) + c**(6))*a**(2) - b**(8) + b**(6)*c**(2) + b**(2)*c**(6) - c**(8))', ID="X_147", classes=["center", "incident"])
            X_185 = eval_trilinear_point(model, A, B, C, '(cos(A))*(1 - cos(A)*cos(B - C))', ID="X_185", classes=["center", "incident"])
            central_line(model, X_147, X_185, 147, 185, incident=True)
            return promote_point_to_top(model, X_3491)


        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_3491 on the given reference triangle."""
            model = create_model('X_3491 = INTERSECTION OF LINES X_1X_295 AND X_4X_69')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03491(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-03491.json"))
            write_center_svg(
                model_acute,
                here / "x-03491.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3491¶

X₃₄₉₁¶