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X₁₅₆₉¶

MOSES-CIRCLE ANTIPODE OF X₁₁₅

X₁₅₆₉ is the moses-circle antipode of X₁₁₅.

X₁₅₆₉ (MOSES-CIRCLE ANTIPODE OF X₁₁₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1569 = MOSES-CIRCLE ANTIPODE OF X_115."""

        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,
            midpoint,
            nine_point_center_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01569(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1569 = MOSES-CIRCLE ANTIPODE OF X_115 on reference triangle ABC."""
            X_99 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(2) - c**(2))', ID="X_99", classes=["center"])
            X_194 = eval_trilinear_point(model, A, B, C, 'b*c*(a**(2)*b**(2) + a**(2)*c**(2) - b**(2)*c**(2))', ID="X_194", classes=["center"])
            X_1569 = midpoint(model, X_99, X_194, ID="X_1569", classes=["selected", "target"], guide=False)
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center", "incident"])
            X_39 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) + c**(2))', ID="X_39", classes=["center", "incident"])
            central_line(model, X_5, X_39, 5, 39, incident=True)
            X_32 = eval_trilinear_point(model, A, B, C, 'a**(3)', ID="X_32", classes=["center", "incident"])
            central_line(model, X_32, X_99, 32, 99, incident=True)
            X_98 = eval_trilinear_point(model, A, B, C, 'sec(A +  omega  )', ID="X_98", classes=["center", "incident"])
            X_574 = eval_trilinear_point(model, A, B, C, 'a*(a**(2) - 2*b**(2) - 2*c**(2))', ID="X_574", classes=["center", "incident"])
            central_line(model, X_98, X_574, 98, 574, incident=True)
            return promote_point_to_top(model, X_1569)


        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_1569 on the given reference triangle."""
            model = create_model('X_1569 = MOSES-CIRCLE ANTIPODE OF X_115')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01569(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-01569.json"))
            write_center_svg(
                model_acute,
                here / "x-01569.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1569¶

X₁₅₆₉¶