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X₁₉₉₀¶

ORTHIC-AXIS INTERCEPT OF LINE X₄X_6

X₁₉₉₀ is described in section 6.4.2 of the downloadable article cited at X₁₉₈₉.

X₁₉₉₀ (ORTHIC-AXIS INTERCEPT OF LINE X₄X_6) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1990 = ORTHIC-AXIS INTERCEPT OF LINE X_4X_6."""

        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,
            midpoint,
            orthocenter_of,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01990(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1990 = ORTHIC-AXIS INTERCEPT OF LINE X_4X_6 on reference triangle ABC."""
            X_297 = eval_trilinear_point(model, A, B, C, 'csc(2*A)*cos(A +  omega  )', ID="X_297", classes=["center"])
            X_648 = eval_trilinear_point(model, A, B, C, '1/(a*(b**(2) - c**(2))*(b**(2) + c**(2) - a**(2)))', ID="X_648", classes=["center"])
            X_1990 = midpoint(model, X_297, X_648, ID="X_1990", classes=["selected", "target"], guide=False)
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            central_line(model, X_4, X_6, 4, 6, incident=True)
            X_50 = eval_trilinear_point(model, A, B, C, 'sin(3*A)', ID="X_50", classes=["center", "incident"])
            X_112 = eval_trilinear_point(model, A, B, C, 'a/(sin(2*B) - sin(2*C))', ID="X_112", classes=["center", "incident"])
            central_line(model, X_50, X_112, 50, 112, incident=True)
            X_140 = eval_trilinear_point(model, A, B, C, '2*cos(A) + cos(B - C)', ID="X_140", classes=["center", "incident"])
            X_216 = eval_trilinear_point(model, A, B, C, 'sin(2*A)*cos(B - C)', ID="X_216", classes=["center", "incident"])
            central_line(model, X_140, X_216, 140, 216, incident=True)
            return promote_point_to_top(model, X_1990)


        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_1990 on the given reference triangle."""
            model = create_model('X_1990 = ORTHIC-AXIS INTERCEPT OF LINE X_4X_6')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01990(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-01990.json"))
            write_center_svg(
                model_acute,
                here / "x-01990.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1990¶

X₁₉₉₀¶