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X₁₂₈₄¶

8th SHARYGIN POINT

X₁₂₈₄ is the homothetic center of the intouch intriangle and the triangle DEF constructed at X₁₂₈₁. Coordinates were found by Jean-Pierre Ehrmann. See Hyacinthos #6293 and #6315.

X₁₂₈₄ (8th SHARYGIN POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1284 = 8th SHARYGIN 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_trilinear_point,
            gergonne_point_of,
            incenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01284(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1284 = 8th SHARYGIN POINT on reference triangle ABC."""
            X_1284 = eval_trilinear_point(model, A, B, C, '((b + c)*(b*c - a**(2))/(b + c - a))', ID="X_1284", classes=["selected", "target"])
            X_7 = gergonne_point_of(model, A, B, C, ID="X_7", classes=["center", "incident"])
            X_21 = eval_trilinear_point(model, A, B, C, '1/(cos(B) + cos(C))', ID="X_21", classes=["center", "incident"])
            central_line(model, X_7, X_21, 7, 21, incident=True)
            X_37 = eval_trilinear_point(model, A, B, C, 'b + c', ID="X_37", classes=["center", "incident"])
            X_65 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C)', ID="X_65", classes=["center", "incident"])
            central_line(model, X_37, X_65, 37, 65, incident=True)
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_256 = eval_trilinear_point(model, A, B, C, '1/(a**(2) + b*c)', ID="X_256", classes=["center", "incident"])
            central_line(model, X_1, X_256, 1, 256, incident=True)
            return promote_point_to_top(model, X_1284)


        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_1284 on the given reference triangle."""
            model = create_model('X_1284 = 8th SHARYGIN POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01284(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-01284.json"))
            write_center_svg(
                model_acute,
                here / "x-01284.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1284¶

X₁₂₈₄¶