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X₃₄₁₃¶

1st KIEPERT INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X₃₄₁₃ lies on the line at infinity.

X₃₄₁₃ (1st KIEPERT INFINITY POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3413 = 1st KIEPERT INFINITY POINT."""

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


        def construct_x_03413(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3413 = 1st KIEPERT INFINITY POINT on reference triangle ABC."""
            X_1379 = point_from_barycentrics(model, A, B, C, -0.11245297, 0.21461865, 0.89783432, ID="X_1379", classes=["center"])
            X_3413 = isogonal_conjugate(model, A, B, C, X_1379, ID="X_3413", classes=["selected", "target"])
            X_30 = eval_trilinear_point(model, A, B, C, 'cos(A) - 2*cos(B)*cos(C)', ID="X_30", classes=["center", "incident"])
            X_511 = eval_trilinear_point(model, A, B, C, 'cos(A +  omega  )', ID="X_511", classes=["center", "incident"])
            central_line(model, X_30, X_511, 30, 511, incident=True)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_1341 = point_from_barycentrics(model, A, B, C, 0.30653192, 0.35355532, 0.33991277, ID="X_1341", classes=["center", "incident"])
            central_line(model, X_2, X_1341, 2, 1341, incident=True)
            X_98 = eval_trilinear_point(model, A, B, C, 'sec(A +  omega  )', ID="X_98", classes=["center", "incident"])
            X_1380 = eval_trilinear_point(model, A, B, C, 'e*cos(A) + cos(A +  omega  )', ID="X_1380", classes=["center", "incident"])
            central_line(model, X_98, X_1380, 98, 1380, incident=True)
            return promote_point_to_top(model, X_3413)


        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_3413 on the given reference triangle."""
            model = create_model('X_3413 = 1st KIEPERT INFINITY POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03413(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-03413.json"))
            write_center_svg(
                model_acute,
                here / "x-03413.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3413¶

X₃₄₁₃¶