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X₃₂₉₁¶

INTERSECTION OF LINES X₂X_39 AND X₂₃₀X_231

Let L denote the line through X₃ perpendicular to the line X₂ X₆. Coefficients for a trilinear equation for L are the trilinears for X₃₂₉₁.

X₃₂₉₁ (INTERSECTION OF LINES X₂X_39 AND X₂₃₀X_231) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3291 = INTERSECTION OF LINES X_2X_39 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_03291(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3291 = INTERSECTION OF LINES X_2X_39 AND X_230X_231 on reference triangle ABC."""
            X_3124 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) - c**(2))**(2)', ID="X_3124", classes=["center"])
            X_3231 = eval_trilinear_point(model, A, B, C, '(a*(2*b**(2)*c**(2) - a**(2)*b**(2) - a**(2)*c**(2)))', ID="X_3231", classes=["center"])
            X_3291 = midpoint(model, X_3124, X_3231, ID="X_3291", classes=["selected", "target"], guide=False)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_39 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) + c**(2))', ID="X_39", classes=["center", "incident"])
            central_line(model, X_2, X_39, 2, 39, incident=True)
            X_23 = eval_trilinear_point(model, A, B, C, 'a*(b**(4) + c**(4) - a**(4) - b**(2)*c**(2))', ID="X_23", classes=["center", "incident"])
            X_111 = eval_trilinear_point(model, A, B, C, 'a/(2*a**(2) - b**(2) - c**(2))', ID="X_111", classes=["center", "incident"])
            central_line(model, X_23, X_111, 23, 111, incident=True)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_373 = eval_trilinear_point(model, A, B, C, '(2*b*c + a*c*cos(C) + a*b*cos(B))', ID="X_373", classes=["center", "incident"])
            central_line(model, X_6, X_373, 6, 373, incident=True)
            return promote_point_to_top(model, X_3291)


        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_3291 on the given reference triangle."""
            model = create_model('X_3291 = INTERSECTION OF LINES X_2X_39 AND X_230X_231')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03291(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-03291.json"))
            write_center_svg(
                model_acute,
                here / "x-03291.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3291¶

X₃₂₉₁¶