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X₁₅₇₇¶

ISOGONAL CONJUGATE OF X₁₆₃

X₁₅₇₇ is the isogonal conjugate of X₁₆₃.

X₁₅₇₇ (ISOGONAL CONJUGATE OF X₁₆₃) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1577 = ISOGONAL CONJUGATE OF X_163."""

        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,
            isogonal_conjugate,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01577(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1577 = ISOGONAL CONJUGATE OF X_163 on reference triangle ABC."""
            X_163 = eval_trilinear_point(model, A, B, C, '(sin(2*A))/(sin(2*B) - sin(2*C))', ID="X_163", classes=["center"])
            X_1577 = isogonal_conjugate(model, A, B, C, X_163, ID="X_1577", classes=["selected", "target"])
            X_240 = eval_trilinear_point(model, A, B, C, 'sec(A)*cos(A +  omega  )', ID="X_240", classes=["center", "incident"])
            X_522 = eval_trilinear_point(model, A, B, C, '(cos(B) - cos(C))*(csc(A))', ID="X_522", classes=["center", "incident"])
            central_line(model, X_240, X_522, 240, 522, incident=True)
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_810 = eval_trilinear_point(model, A, B, C, 'sin(2*A)*((cos(B))**(2) - (cos(C))**(2))', ID="X_810", classes=["center", "incident"])
            central_line(model, X_1, X_810, 1, 810, incident=True)
            X_784 = eval_trilinear_point(model, A, B, C, '(a **(-4)*(b **(-2) - c **(-2)) + a **(-3)*(b **(-3) - c **(-3)))', ID="X_784", classes=["center", "incident"])
            X_149 = eval_trilinear_point(model, A, B, C, '(b*c*(b**(3) + c**(3) - a**(3) + (a**(2) - b*c)*(b + c) + a*(b*c - b**(2) - c**(2))))', ID="X_149", classes=["center", "incident"])
            central_line(model, X_784, X_149, 784, 149, incident=True)
            return promote_point_to_top(model, X_1577)


        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_1577 on the given reference triangle."""
            model = create_model('X_1577 = ISOGONAL CONJUGATE OF X_163')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01577(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-01577.json"))
            write_center_svg(
                model_acute,
                here / "x-01577.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1577¶

X₁₅₇₇¶