← etc / Encyclopedia of Triangle Centers

X₇₆₁¶

EVEN (1, 4) CIRCUMCIRCLE POINT

X₇₆₁ (EVEN (1, 4) CIRCUMCIRCLE POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_761 = EVEN (1, 4) CIRCUMCIRCLE 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,
            isogonal_conjugate,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00761(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_761 = EVEN (1, 4) CIRCUMCIRCLE POINT on reference triangle ABC."""
            X_760 = eval_trilinear_point(model, A, B, C, '(a**(0)*(b**(4) + c**(4)) - a**(3)*(b**(1) + c**(1)))', ID="X_760", classes=["center"])
            X_761 = isogonal_conjugate(model, A, B, C, X_760, ID="X_761", classes=["selected", "target"])
            X_665 = eval_trilinear_point(model, A, B, C, 'a*((a - b)**(2)*(a + b - c) - (c - a)**(2)*(c + a - b))', ID="X_665", classes=["center", "incident"])
            X_743 = eval_trilinear_point(model, A, B, C, '(1/(a **(-2)*(b**(2) + c**(2)) - a**(1)*(b **(-1) + c **(-1))))', ID="X_743", classes=["center", "incident"])
            central_line(model, X_665, X_743, 665, 743, incident=True)
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_825 = eval_trilinear_point(model, A, B, C, '1/(a**(-1)*(b**(3) - c**(3)) + a**(2)*(b**(0) - c**(0)))', ID="X_825", classes=["center", "incident"])
            central_line(model, X_1, X_825, 1, 825, incident=True)
            X_76 = eval_trilinear_point(model, A, B, C, '1/a**(3)', ID="X_76", classes=["center", "incident"])
            X_789 = eval_trilinear_point(model, A, B, C, 'a **(- 2)/(b**(3) - c**(3))', ID="X_789", classes=["center", "incident"])
            central_line(model, X_76, X_789, 76, 789, incident=True)
            return promote_point_to_top(model, X_761)


        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_761 on the given reference triangle."""
            model = create_model('X_761 = EVEN (1, 4) CIRCUMCIRCLE POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00761(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-00761.json"))
            write_center_svg(
                model_acute,
                here / "x-00761.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X761¶

X₇₆₁¶