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X₁₃₂₇¶

ARCTAN(3) KIEPERT POINT

Let \(BB_{A}\)C_AC be the external square on side BC, and define \(CC_{B}\)A_BA and \(AA_{C}\)B_CB cyclically. The lines A_BB_A, B_CC_B, C_AA_C form a triangle perspective to triangle ABC, and the perspector is X₁₃₂₇.

X₁₃₂₇ (ARCTAN(3) KIEPERT POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1327 = ARCTAN(3) KIEPERT 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,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01327(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1327 = ARCTAN(3) KIEPERT POINT on reference triangle ABC."""
            X_1327 = eval_trilinear_point(model, A, B, C, '(1/(sin(A) + 3*cos(A)))', ID="X_1327", 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_485 = eval_trilinear_point(model, A, B, C, 'sec(A -  pi  /4)', ID="X_485", classes=["center", "incident"])
            central_line(model, X_30, X_485, 30, 485, incident=True)
            X_381 = eval_trilinear_point(model, A, B, C, '2*cos(B - C) - cos(A)', ID="X_381", classes=["center", "incident"])
            X_486 = eval_trilinear_point(model, A, B, C, 'sec(A +  pi  /4)', ID="X_486", classes=["center", "incident"])
            central_line(model, X_381, X_486, 381, 486, incident=True)
            X_371 = eval_trilinear_point(model, A, B, C, 'cos(A -  pi  /4)', ID="X_371", classes=["center", "incident"])
            X_1131 = eval_trilinear_point(model, A, B, C, '1/(sin(A) + 2*cos(A))', ID="X_1131", classes=["center", "incident"])
            central_line(model, X_371, X_1131, 371, 1131, incident=True)
            return promote_point_to_top(model, X_1327)


        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_1327 on the given reference triangle."""
            model = create_model('X_1327 = ARCTAN(3) KIEPERT POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01327(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-01327.json"))
            write_center_svg(
                model_acute,
                here / "x-01327.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1327¶

X₁₃₂₇¶