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X₃₀₅₆¶

INTERSECTION OF LINES X₁X_256 AND X₆X_31

X₃₀₅₆ = reflection of X₁₄₆₉ in X₁

X₃₀₅₆ (INTERSECTION OF LINES X₁X_256 AND X₆X_31) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3056 = INTERSECTION OF LINES X_1X_256 AND X_6X_31."""

        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,
            feuerbach_point_of,
            incenter_of,
            promote_point_to_top,
            reflection_in_point,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03056(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3056 = INTERSECTION OF LINES X_1X_256 AND X_6X_31 on reference triangle ABC."""
            X_1469 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) + b*c + c**(2))/(a - b - c)', ID="X_1469", classes=["center"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center"])
            X_3056 = reflection_in_point(model, X_1469, X_1, ID="X_3056", classes=["selected", "target"], guide=False)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_31 = eval_trilinear_point(model, A, B, C, 'a**(2)', ID="X_31", classes=["center", "incident"])
            central_line(model, X_6, X_31, 6, 31, incident=True)
            X_11 = feuerbach_point_of(model, A, B, C, ID="X_11", 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_11, X_141, 11, 141, incident=True)
            X_35 = eval_trilinear_point(model, A, B, C, '1 + 2*cos(A)', ID="X_35", classes=["center", "incident"])
            X_182 = eval_trilinear_point(model, A, B, C, 'cos(A-  omega  )', ID="X_182", classes=["center", "incident"])
            central_line(model, X_35, X_182, 35, 182, incident=True)
            return promote_point_to_top(model, X_3056)


        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_3056 on the given reference triangle."""
            model = create_model('X_3056 = INTERSECTION OF LINES X_1X_256 AND X_6X_31')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03056(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-03056.json"))
            write_center_svg(
                model_acute,
                here / "x-03056.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3056¶

X₃₀₅₆¶