← etc / Encyclopedia of Triangle Centers

X₁₈₉₉¶

ZOSMA TRANSFORM OF X₁₀₉₆

X₁₈₉₉ = reflection of X₃₉₄ in X₁₃₆₈

X₁₈₉₉ (ZOSMA TRANSFORM OF X₁₀₉₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1899 = ZOSMA TRANSFORM OF X_1096."""

        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,
            orthocenter_of,
            promote_point_to_top,
            reflection_in_point,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01899(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1899 = ZOSMA TRANSFORM OF X_1096 on reference triangle ABC."""
            X_394 = eval_trilinear_point(model, A, B, C, 'cos(A)*cot(A)', ID="X_394", classes=["center"])
            X_1368 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2)/(a**(2) - b**(2) + c**(2)) + c**(2)/(a**(2) + b**(2) - c**(2)))', ID="X_1368", classes=["center"])
            X_1899 = reflection_in_point(model, X_394, X_1368, ID="X_1899", classes=["selected", "target"], guide=False)
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_51 = eval_trilinear_point(model, A, B, C, 'a**(2)*cos(B - C)', ID="X_51", classes=["center", "incident"])
            central_line(model, X_4, X_51, 4, 51, incident=True)
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_68 = eval_trilinear_point(model, A, B, C, 'cos(A)*sec(2*A)', ID="X_68", classes=["center", "incident"])
            central_line(model, X_3, X_68, 3, 68, incident=True)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_66 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(4) + c**(4) - a**(4))', ID="X_66", classes=["center", "incident"])
            central_line(model, X_6, X_66, 6, 66, incident=True)
            return promote_point_to_top(model, X_1899)


        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_1899 on the given reference triangle."""
            model = create_model('X_1899 = ZOSMA TRANSFORM OF X_1096')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01899(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-01899.json"))
            write_center_svg(
                model_acute,
                here / "x-01899.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1899¶

X₁₈₉₉¶