← etc / Encyclopedia of Triangle Centers

X₂₂₂₅¶

X₂-ISOCONJUGATE OF X₆₇₅

X₂₂₂₅ = crosssum of X₁ and X₂₂₂₅

X₂₂₂₅ (X₂-ISOCONJUGATE OF X₆₇₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2225 = X_2-ISOCONJUGATE OF X_675."""

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


        def construct_x_02225(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2225 = X_2-ISOCONJUGATE OF X_675 on reference triangle ABC."""
            X_31 = eval_trilinear_point(model, A, B, C, 'a**(2)', ID="X_31", classes=["center"])
            X_32 = eval_trilinear_point(model, A, B, C, 'a**(3)', ID="X_32", classes=["center"])
            X_63 = eval_trilinear_point(model, A, B, C, 'cot(A)', ID="X_63", classes=["center"])
            X_169 = eval_trilinear_point(model, A, B, C, '- (sin(A))*(cos(A/2))**(2) + (sin(B))*(cos(B/2))**(2) + (sin(C))*(cos(C/2))**(2)', ID="X_169", classes=["center"])
            central_line(model, X_31, X_32, 31, 32)
            central_line(model, X_63, X_169, 63, 169)
            X_2225 = intersect_lines(model, X_31, X_32, X_63, X_169, ID="X_2225", classes=["selected", "target"])
            X_44 = eval_trilinear_point(model, A, B, C, 'b + c - 2*a', ID="X_44", classes=["center", "incident"])
            X_513 = eval_trilinear_point(model, A, B, C, 'b - c', ID="X_513", classes=["center", "incident"])
            central_line(model, X_44, X_513, 44, 513, incident=True)
            return promote_point_to_top(model, X_2225)


        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_2225 on the given reference triangle."""
            model = create_model('X_2225 = X_2-ISOCONJUGATE OF X_675')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02225(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-02225.json"))
            write_center_svg(
                model_acute,
                here / "x-02225.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2225¶

X₂₂₂₅¶