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X₁₆₅₇¶

{X₃,X₄}-HARMONIC CONJUGATE OF X₁₆₅₆

X₁₆₅₇ is the {X₃,X₄}-harmonic conjugate of X₁₆₅₆.

X₁₆₅₇ ({X₃,X₄}-HARMONIC CONJUGATE OF X₁₆₅₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1657 = {X_3,X_4}-HARMONIC CONJUGATE OF X_1656."""

        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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01657(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1657 = {X_3,X_4}-HARMONIC CONJUGATE OF X_1656 on reference triangle ABC."""
            X_1657 = eval_trilinear_point(model, A, B, C, '3*cos(A) - 4*cos(B)*cos(C)', ID="X_1657", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            central_line(model, X_2, X_3, 2, 3)
            X_195 = eval_trilinear_point(model, A, B, C, 'a*(a**(8) + b**(8) + c**(8) - 4*a**(6)*(b**(2) + c**(2)) + a**(4)*(6*b**(4) + 6*c**(4) + 5*b**(2)*c**(2)) - a**(2)*(4*b**(6) + 4*c**(6) - b**(4)*c**(2) - b**(2)*c**(4)) - 2*b**(2)*c**(2)*(b**(4) + c**(4) - b**(2)*c**(2)))', ID="X_195", classes=["center", "incident"])
            X_1181 = eval_trilinear_point(model, A, B, C, '((1 - cos(A)*sin(B)*sin(C))*cos(A))', ID="X_1181", classes=["center", "incident"])
            central_line(model, X_195, X_1181, 195, 1181, incident=True)
            X_399 = eval_trilinear_point(model, A, B, C, '5*cos(A) - 4*cos(B)*cos(C) - 8*sin(B)*sin(C)*(cos(A))**(2)', ID="X_399", classes=["center", "incident"])
            X_1498 = eval_trilinear_point(model, A, B, C, '(sin(A))*((tan(B))**(2) + (tan(C))**(2) - (tan(A))**(2))', ID="X_1498", classes=["center", "incident"])
            central_line(model, X_399, X_1498, 399, 1498, incident=True)
            return promote_point_to_top(model, X_1657)


        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_1657 on the given reference triangle."""
            model = create_model('X_1657 = {X_3,X_4}-HARMONIC CONJUGATE OF X_1656')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01657(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-01657.json"))
            write_center_svg(
                model_acute,
                here / "x-01657.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1657¶

X₁₆₅₇¶