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X₁₉₈₆¶

HATZIPOLAKIS REFLECTION POINT

Let H_aH_bH_c be the orthic triangle of triangle ABC. Let A_B be the reflection of A in H_c, and define A_C, B_C, B_A, C_A, C_B functionally. Then the nine-point circles of the triangles

X₁₉₈₆ (HATZIPOLAKIS REFLECTION POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1986 = HATZIPOLAKIS REFLECTION 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,
            ceva_conjugate,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            orthocenter_of,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01986(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1986 = HATZIPOLAKIS REFLECTION POINT on reference triangle ABC."""
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center"])
            X_403 = eval_trilinear_point(model, A, B, C, '(sec(A))*(1 + cos(2*B) + cos(2*C))', ID="X_403", classes=["center"])
            X_1986 = ceva_conjugate(model, A, B, C, X_4, X_403, ID="X_1986", classes=["selected", "target"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_74 = eval_trilinear_point(model, A, B, C, '1/(cos(A) - 2*cos(B)*cos(C))', ID="X_74", classes=["center", "incident"])
            central_line(model, X_6, X_74, 6, 74, incident=True)
            X_94 = eval_trilinear_point(model, A, B, C, 'csc(3*A)', ID="X_94", classes=["center", "incident"])
            central_line(model, X_4, X_94, 4, 94, incident=True)
            X_24 = eval_trilinear_point(model, A, B, C, 'sec(A)*cos(2*A)', ID="X_24", classes=["center", "incident"])
            X_110 = eval_trilinear_point(model, A, B, C, 'csc(B - C)', ID="X_110", classes=["center", "incident"])
            central_line(model, X_24, X_110, 24, 110, incident=True)
            return promote_point_to_top(model, X_1986)


        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_1986 on the given reference triangle."""
            model = create_model('X_1986 = HATZIPOLAKIS REFLECTION POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01986(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-01986.json"))
            write_center_svg(
                model_acute,
                here / "x-01986.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1986¶

X₁₉₈₆¶