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X₂₁₀₈¶

POINT KEPLER I

X₂₁₀₈ = perspector of 2nd Sharygin triangle and unary cofactor triangle of 1st Sharygin triangle

X₂₁₀₈ (POINT KEPLER I) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2108 = POINT KEPLER I."""

        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,
            incenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02108(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2108 = POINT KEPLER I on reference triangle ABC."""
            X_2108 = eval_trilinear_point(model, A, B, C, '((b + c)*a**(3) - (b**(2) - b*c + c**(2))*a**(2) - (b + c)*(b**(2) + c**(2))*a + b*c*(b**(2) + b*c + c**(2)))', ID="X_2108", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", 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_1, X_39, 1, 39, incident=True)
            X_31 = eval_trilinear_point(model, A, B, C, 'a**(2)', ID="X_31", classes=["center", "incident"])
            X_43 = eval_trilinear_point(model, A, B, C, 'a*b + a*c - b*c', ID="X_43", classes=["center", "incident"])
            central_line(model, X_31, X_43, 31, 43, incident=True)
            X_170 = eval_trilinear_point(model, A, B, C, '(- (tan(A/2))*(sec(A/2))**(2) + (tan(B/2))*(sec(B/2))**(2) + (tan(C/2))*(sec(C/2))**(2))', ID="X_170", classes=["center", "incident"])
            X_411 = eval_trilinear_point(model, A, B, C, '(cos(B)*cos(C) - (cos(A) + cos(B) + cos(C))*cos(A))', ID="X_411", classes=["center", "incident"])
            central_line(model, X_170, X_411, 170, 411, incident=True)
            return promote_point_to_top(model, X_2108)


        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_2108 on the given reference triangle."""
            model = create_model('X_2108 = POINT KEPLER I')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02108(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-02108.json"))
            write_center_svg(
                model_acute,
                here / "x-02108.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2108¶

X₂₁₀₈¶