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X₈₇₄¶

INTERSECTION OF LINES X₁X_75 AND X₉₉X_670

X₈₇₄ (INTERSECTION OF LINES X₁X_75 AND X₉₉X_670) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_874 = INTERSECTION OF LINES X_1X_75 AND X_99X_670."""

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


        def construct_x_00874(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_874 = INTERSECTION OF LINES X_1X_75 AND X_99X_670 on reference triangle ABC."""
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center"])
            X_75 = eval_trilinear_point(model, A, B, C, '1/a**(2)', ID="X_75", classes=["center"])
            X_99 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(2) - c**(2))', ID="X_99", classes=["center"])
            X_670 = eval_trilinear_point(model, A, B, C, '1/(a**(3)*(b**(2) - c**(2)))', ID="X_670", classes=["center"])
            central_line(model, X_1, X_75, 1, 75)
            central_line(model, X_99, X_670, 99, 670)
            X_874 = intersect_lines(model, X_1, X_75, X_99, X_670, ID="X_874", classes=["selected", "target"])
            X_190 = eval_trilinear_point(model, A, B, C, 'b*c/(b - c)', ID="X_190", classes=["center", "incident"])
            X_646 = eval_trilinear_point(model, A, B, C, '((b + c - a)/(a**(2)*(b - c)))', ID="X_646", classes=["center", "incident"])
            central_line(model, X_190, X_646, 190, 646, incident=True)
            return promote_point_to_top(model, X_874)


        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_874 on the given reference triangle."""
            model = create_model('X_874 = INTERSECTION OF LINES X_1X_75 AND X_99X_670')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00874(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-00874.json"))
            write_center_svg(
                model_acute,
                here / "x-00874.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X874¶

X₈₇₄¶