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X₁₉₉₈¶

ORTHOCORRESPONDENT OF X₉

X₁₉₉₈ (ORTHOCORRESPONDENT OF X₉) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1998 = ORTHOCORRESPONDENT OF X_9."""

        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,
            incenter_of,
            intersect_lines,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01998(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1998 = ORTHOCORRESPONDENT OF X_9 on reference triangle ABC."""
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_57 = eval_trilinear_point(model, A, B, C, '1/(b + c - a)', ID="X_57", classes=["center"])
            X_1004 = eval_trilinear_point(model, A, B, C, 'a**(5) - 2*a**(4)*(b + c) + 2*a**(2)*(b**(3) + c**(3)) - a*(b**(2) + c**(2))**(2) + 2*b*c*(b - c)*(b**(2) - c**(2))', ID="X_1004", classes=["center"])
            central_line(model, X_1, X_2, 1, 2)
            central_line(model, X_57, X_1004, 57, 1004)
            X_1998 = intersect_lines(model, X_1, X_2, X_57, X_1004, ID="X_1998", classes=["selected", "target"])
            X_63 = eval_trilinear_point(model, A, B, C, 'cot(A)', ID="X_63", classes=["center", "incident"])
            X_1005 = point_from_barycentrics(model, A, B, C, 0.38047896, 0.36259614, 0.2569249, ID="X_1005", classes=["center", "incident"])
            central_line(model, X_63, X_1005, 63, 1005, incident=True)
            return promote_point_to_top(model, X_1998)


        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_1998 on the given reference triangle."""
            model = create_model('X_1998 = ORTHOCORRESPONDENT OF X_9')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01998(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-01998.json"))
            write_center_svg(
                model_acute,
                here / "x-01998.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1998¶

X₁₉₉₈¶