← etc / Encyclopedia of Triangle Centers

X₁₂₁₄¶

ISOGONAL CONJUGATE OF X₁₁₇₂

X₁₂₁₄ is the isogonal conjugate of X₁₁₇₂.

X₁₂₁₄ (ISOGONAL CONJUGATE OF X₁₁₇₂) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1214 = ISOGONAL CONJUGATE OF X_1172."""

        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,
            centroid_of,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            incenter_of,
            isogonal_conjugate,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01214(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1214 = ISOGONAL CONJUGATE OF X_1172 on reference triangle ABC."""
            X_1172 = point_from_barycentrics(model, A, B, C, 0.14979394, 0.23060383, 0.61960222, ID="X_1172", classes=["center"])
            X_1214 = isogonal_conjugate(model, A, B, C, X_1172, ID="X_1214", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            central_line(model, X_1, X_3, 1, 3, incident=True)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_92 = eval_trilinear_point(model, A, B, C, 'csc(2*A)', ID="X_92", classes=["center", "incident"])
            central_line(model, X_2, X_92, 2, 92, incident=True)
            X_63 = eval_trilinear_point(model, A, B, C, 'cot(A)', ID="X_63", classes=["center", "incident"])
            X_77 = eval_trilinear_point(model, A, B, C, '1/(1 + sec(A))', ID="X_77", classes=["center", "incident"])
            central_line(model, X_63, X_77, 63, 77, incident=True)
            return promote_point_to_top(model, X_1214)


        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_1214 on the given reference triangle."""
            model = create_model('X_1214 = ISOGONAL CONJUGATE OF X_1172')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01214(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-01214.json"))
            write_center_svg(
                model_acute,
                here / "x-01214.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1214¶

X₁₂₁₄¶