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X₃₀₈₅¶

INTERSECTION OF LINES X₁X_2 AND X₄X_12

X₃₀₈₅ = {X₁,X₂}-harmonic conjugate of X₃₀₈₆

X₃₀₈₅ (INTERSECTION OF LINES X₁X_2 AND X₄X_12) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3085 = INTERSECTION OF LINES X_1X_2 AND X_4X_12."""

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


        def construct_x_03085(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3085 = INTERSECTION OF LINES X_1X_2 AND X_4X_12 on reference triangle ABC."""
            X_3085 = eval_trilinear_point(model, A, B, C, '(1 + sin(B)*sin(C))', ID="X_3085", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            central_line(model, X_1, X_2, 1, 2, incident=True)
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_12 = eval_trilinear_point(model, A, B, C, '1 + cos(B - C)', ID="X_12", classes=["center", "incident"])
            central_line(model, X_4, X_12, 4, 12, incident=True)
            X_7 = gergonne_point_of(model, A, B, C, ID="X_7", classes=["center", "incident"])
            X_46 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C) - cos(A)', ID="X_46", classes=["center", "incident"])
            central_line(model, X_7, X_46, 7, 46, incident=True)
            return promote_point_to_top(model, X_3085)


        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_3085 on the given reference triangle."""
            model = create_model('X_3085 = INTERSECTION OF LINES X_1X_2 AND X_4X_12')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03085(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-03085.json"))
            write_center_svg(
                model_acute,
                here / "x-03085.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3085¶

X₃₀₈₅¶