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X₁₂₈₂¶

5th SHARYGIN POINT

X₁₂₈₂ is the perspector of the excentral triangle and the triangle D'E'F' constructed at X₁₂₈₁. Coordinates were found by Jean-Pierre Ehrmann. See Hyacinthos #6293 and #6315.

X₁₂₈₂ (5th SHARYGIN POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1282 = 5th 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,
            incenter_of,
            intersect_lines,
            promote_point_to_top,
            spieker_center_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01282(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1282 = 5th SHARYGIN POINT on reference triangle ABC."""
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center"])
            X_41 = eval_trilinear_point(model, A, B, C, 'a**(2)*(b + c - a)', ID="X_41", classes=["center"])
            X_43 = eval_trilinear_point(model, A, B, C, 'a*b + a*c - b*c', ID="X_43", classes=["center"])
            X_57 = eval_trilinear_point(model, A, B, C, '1/(b + c - a)', ID="X_57", classes=["center"])
            central_line(model, X_1, X_41, 1, 41)
            central_line(model, X_43, X_57, 43, 57)
            X_1282 = intersect_lines(model, X_1, X_41, X_43, X_57, ID="X_1282", classes=["selected", "target"])
            X_10 = spieker_center_of(model, A, B, C, ID="X_10", classes=["center", "incident"])
            X_150 = eval_trilinear_point(model, A, B, C, '(b*c*(b**(4) + c**(4) - a**(4) + a*(b*c**(2) +c*b**(2) - b**(3) - c**(3)) - b*c*(a**(2) + b**(2) + c**(2)) + (b + c)*a**(3)))', ID="X_150", classes=["center", "incident"])
            central_line(model, X_10, X_150, 10, 150, incident=True)
            return promote_point_to_top(model, X_1282)


        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_1282 on the given reference triangle."""
            model = create_model('X_1282 = 5th SHARYGIN POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01282(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-01282.json"))
            write_center_svg(
                model_acute,
                here / "x-01282.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1282¶

X₁₂₈₂¶