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X₃₆₃₈¶

INNER SODDY-GERGONNE POINT

Write I = X₁, U = X₇, r = inradius, R = circumradius, and d = 4*\(\sqrt{3}\)*area(ABC). Then distance ratios are given by |IP|/|PU| = 2r(r + 4R)/d and |IQ|/|QU| = -2r(r + 4R)/d

X₃₆₃₈ (INNER SODDY-GERGONNE POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3638 = INNER SODDY-GERGONNE 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_barycentric_point,
            eval_trilinear_point,
            gergonne_point_of,
            incenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03638(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3638 = INNER SODDY-GERGONNE POINT on reference triangle ABC."""
            X_3638 = eval_barycentric_point(model, A, B, C, '(-2*(2*a**(2)-(b+c)*a-(b-c)**(2))*S+sqrt(3)*(-a+b+c) * (2*a**(3)-(b+c)*a**(2)-(b**(2)-c**(2)) * (b-c))) * (a-b+c) * (a+b-c)', ID="X_3638", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_7 = gergonne_point_of(model, A, B, C, ID="X_7", classes=["center", "incident"])
            central_line(model, X_1, X_7, 1, 7, incident=True)
            X_14 = eval_trilinear_point(model, A, B, C, 'csc(A -  pi  /3)', ID="X_14", classes=["center", "incident"])
            X_226 = eval_trilinear_point(model, A, B, C, '(csc(A))*(cos(B) + cos(C))', ID="X_226", classes=["center", "incident"])
            central_line(model, X_14, X_226, 14, 226, incident=True)
            X_57 = eval_trilinear_point(model, A, B, C, '1/(b + c - a)', ID="X_57", classes=["center", "incident"])
            X_1277 = eval_trilinear_point(model, A, B, C, '(sqrt(3/4) - sin(A -  pi  /3) + sin(B -  pi  /3) + sin(C -  pi  /3))', ID="X_1277", classes=["center", "incident"])
            central_line(model, X_57, X_1277, 57, 1277, incident=True)
            return promote_point_to_top(model, X_3638)


        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_3638 on the given reference triangle."""
            model = create_model('X_3638 = INNER SODDY-GERGONNE POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03638(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-03638.json"))
            write_center_svg(
                model_acute,
                here / "x-03638.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3638¶

X₃₆₃₈¶