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X₃₂₉₀¶

INTERSECTION OF LINES X₂X_37 AND X₂₃₀X_231

Let L denote the line through X₃ perpendicular to the line X₁ X₆. Coefficients for a trilinear equation for L are the trilinears for X₃₂₉₀.

X₃₂₉₀ (INTERSECTION OF LINES X₂X_37 AND X₂₃₀X_231) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3290 = INTERSECTION OF LINES X_2X_37 AND X_230X_231."""

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


        def construct_x_03290(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3290 = INTERSECTION OF LINES X_2X_37 AND X_230X_231 on reference triangle ABC."""
            X_3125 = eval_trilinear_point(model, A, B, C, '((b + c)*(b - c)**(2))', ID="X_3125", classes=["center"])
            X_3230 = eval_trilinear_point(model, A, B, C, '(a*(2*b*c - a*b - a*c))', ID="X_3230", classes=["center"])
            X_3290 = midpoint(model, X_3125, X_3230, ID="X_3290", classes=["selected", "target"], guide=False)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_37 = eval_trilinear_point(model, A, B, C, 'b + c', ID="X_37", classes=["center", "incident"])
            central_line(model, X_2, X_37, 2, 37, incident=True)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_354 = eval_trilinear_point(model, A, B, C, '(b - c)**(2) - a*b - a*c', ID="X_354", classes=["center", "incident"])
            central_line(model, X_6, X_354, 6, 354, incident=True)
            X_230 = eval_trilinear_point(model, A, B, C, 'b*c*(a**(2)*(2*a**(2) - b**(2) - c**(2)) + (b**(2) - c**(2))**(2))', ID="X_230", classes=["center", "incident"])
            X_231 = eval_trilinear_point(model, A, B, C, '(cos(B))*(4*(sin(C))**(2) - 1)*(cos(A)*sin(B) - sin(A)*cos(B)) - (cos(C))*(4*(sin(B))**(2) - 1)*(cos(C)*sin(A) - sin(C)*cos(A))', ID="X_231", classes=["center", "incident"])
            central_line(model, X_230, X_231, 230, 231, incident=True)
            return promote_point_to_top(model, X_3290)


        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_3290 on the given reference triangle."""
            model = create_model('X_3290 = INTERSECTION OF LINES X_2X_37 AND X_230X_231')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03290(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-03290.json"))
            write_center_svg(
                model_acute,
                here / "x-03290.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3290¶

X₃₂₉₀¶