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X₁₂₁₂¶

ISOGONAL CONJUGATE OF X₁₁₇₀

X₁₂₁₂ is the isogonal conjugate of X₁₁₇₀.

X₁₂₁₂ (ISOGONAL CONJUGATE OF X₁₁₇₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1212 = ISOGONAL CONJUGATE OF X_1170."""

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


        def construct_x_01212(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1212 = ISOGONAL CONJUGATE OF X_1170 on reference triangle ABC."""
            X_1170 = eval_trilinear_point(model, A, B, C, '1/((a - b - c)*(a*(b + c) - (b - c)**(2)))', ID="X_1170", classes=["center"])
            X_1212 = isogonal_conjugate(model, A, B, C, X_1170, ID="X_1212", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            central_line(model, X_1, X_6, 1, 6, incident=True)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_85 = eval_trilinear_point(model, A, B, C, 'b**(2)*c**(2)/(b + c - a)', ID="X_85", classes=["center", "incident"])
            central_line(model, X_2, X_85, 2, 85, incident=True)
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            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", "incident"])
            central_line(model, X_3, X_169, 3, 169, incident=True)
            return promote_point_to_top(model, X_1212)


        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_1212 on the given reference triangle."""
            model = create_model('X_1212 = ISOGONAL CONJUGATE OF X_1170')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01212(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-01212.json"))
            write_center_svg(
                model_acute,
                here / "x-01212.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1212¶

X₁₂₁₂¶