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X₁₁₅₇¶

INVERSE-IN-CIRCUMCIRCLE OF X₅₄

For any point X, let X_A be the reflection of X in sideline BC, and define X_B and X_C cyclically. Then X₁₁₅₇ is the unique point X for which the lines AX_A, BX_B, CX_C concur on the circumcircle; the point of concurrence is X₁₁₄₁.

X₁₁₅₇ (INVERSE-IN-CIRCUMCIRCLE OF X₅₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1157 = INVERSE-IN-CIRCUMCIRCLE OF X_54."""

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


        def construct_x_01157(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1157 = INVERSE-IN-CIRCUMCIRCLE OF X_54 on reference triangle ABC."""
            X_1157 = eval_trilinear_point(model, A, B, C, '4*cos(A) + cos(3*A)*sec(A)*sec(B - C)', ID="X_1157", classes=["selected", "target"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_54 = eval_trilinear_point(model, A, B, C, 'sec(B - C)', ID="X_54", classes=["center", "incident"])
            central_line(model, X_3, X_54, 3, 54, incident=True)
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center", "incident"])
            X_252 = eval_trilinear_point(model, A, B, C, '(sec(B - C)/(1 - 2*cos(2*A)))', ID="X_252", classes=["center", "incident"])
            central_line(model, X_5, X_252, 5, 252, incident=True)
            X_186 = eval_trilinear_point(model, A, B, C, '4*cos(A) - sec(A)', ID="X_186", classes=["center", "incident"])
            X_933 = eval_trilinear_point(model, A, B, C, 'sec(A)*csc(2*B - 2*C)', ID="X_933", classes=["center", "incident"])
            central_line(model, X_186, X_933, 186, 933, incident=True)
            return promote_point_to_top(model, X_1157)


        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_1157 on the given reference triangle."""
            model = create_model('X_1157 = INVERSE-IN-CIRCUMCIRCLE OF X_54')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01157(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-01157.json"))
            write_center_svg(
                model_acute,
                here / "x-01157.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1157¶

X₁₁₅₇¶