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X₃₃₃₃¶

POHOATA POINT

Let R be the circumradius, r the inradius, and \(r_{A}\) the radius of the A-excircle. The trilinears given above are equivalent to 2R - \(r_{A}\) : 2R - \(r_{B}\) : 2R - \(r_{C}\). The 1st trilinear representation

X₃₃₃₃ (POHOATA POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3333 = POHOATA 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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            gergonne_point_of,
            incenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03333(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3333 = POHOATA POINT on reference triangle ABC."""
            X_3333 = eval_trilinear_point(model, A, B, C, '(a - b + c)*(a + b - c)*(a + b + c) + 4*a*b*c', ID="X_3333", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            central_line(model, X_1, X_3, 1, 3, incident=True)
            X_7 = gergonne_point_of(model, A, B, C, ID="X_7", classes=["center", "incident"])
            X_84 = eval_trilinear_point(model, A, B, C, '1/(cos(B) + cos(C) - cos(A) - 1)', ID="X_84", classes=["center", "incident"])
            central_line(model, X_7, X_84, 7, 84, incident=True)
            X_200 = eval_trilinear_point(model, A, B, C, '(cot(A/2))**(2)', ID="X_200", classes=["center", "incident"])
            X_474 = eval_trilinear_point(model, A, B, C, 'cos(A) - (a + b + c)/a', ID="X_474", classes=["center", "incident"])
            central_line(model, X_200, X_474, 200, 474, incident=True)
            return promote_point_to_top(model, X_3333)


        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_3333 on the given reference triangle."""
            model = create_model('X_3333 = POHOATA POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03333(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-03333.json"))
            write_center_svg(
                model_acute,
                here / "x-03333.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3333¶

X₃₃₃₃¶