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X₁₈₇¶

INVERSE-IN-CIRCUMCIRCLE OF X₆ (SCHOUTE CENTER)

Let L denote the line having trilinears of X₁₈₇ as coefficients. Then L is the line passing through X₂ perpendicular to the Euler line.

X₁₈₇ (INVERSE-IN-CIRCUMCIRCLE OF X₆ (SCHOUTE CENTER)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_187 = INVERSE-IN-CIRCUMCIRCLE OF X_6 (SCHOUTE CENTER)."""

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


        def construct_x_00187(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_187 = INVERSE-IN-CIRCUMCIRCLE OF X_6 (SCHOUTE CENTER) on reference triangle ABC."""
            X_187 = eval_trilinear_point(model, A, B, C, 'a*(2*a**(2) - b**(2) - c**(2))', ID="X_187", classes=["selected", "target"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            central_line(model, X_3, X_6, 3, 6, incident=True)
            X_23 = eval_trilinear_point(model, A, B, C, 'a*(b**(4) + c**(4) - a**(4) - b**(2)*c**(2))', ID="X_23", classes=["center", "incident"])
            X_111 = eval_trilinear_point(model, A, B, C, 'a/(2*a**(2) - b**(2) - c**(2))', ID="X_111", classes=["center", "incident"])
            central_line(model, X_23, X_111, 23, 111, incident=True)
            X_30 = eval_trilinear_point(model, A, B, C, 'cos(A) - 2*cos(B)*cos(C)', ID="X_30", classes=["center", "incident"])
            X_115 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2) - c**(2))**(2)', ID="X_115", classes=["center", "incident"])
            central_line(model, X_30, X_115, 30, 115, incident=True)
            return promote_point_to_top(model, X_187)


        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_187 on the given reference triangle."""
            model = create_model('X_187 = INVERSE-IN-CIRCUMCIRCLE OF X_6 (SCHOUTE CENTER)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00187(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-00187.json"))
            write_center_svg(
                model_acute,
                here / "x-00187.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X187¶

X₁₈₇¶