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X₁₉₉₂¶

ORTHOCORRESPONDENT OF X₂

Let H_aH_bH_c be the orthic triangle. X₁₉₉₂ is the radical center of the 2nd Lemoine circles of triangles AH_bH_c, BH_cH_a, CH_aH_b. (Randy Hutson, July 31 2018)

X₁₉₉₂ (ORTHOCORRESPONDENT OF X₂) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1992 = ORTHOCORRESPONDENT OF X_2."""

        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,
            construct_baseline_triangle,
            create_model,
            eval_barycentric_point,
            eval_trilinear_point,
            midpoint,
            orthocenter_of,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01992(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1992 = ORTHOCORRESPONDENT OF X_2 on reference triangle ABC."""
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_193 = eval_trilinear_point(model, A, B, C, '(csc(A))*(cot(B) + cot(C) - cot(A))', ID="X_193", classes=["center"])
            X_1992 = midpoint(model, X_2, X_193, ID="X_1992", classes=["selected", "target"], guide=False)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            central_line(model, X_2, X_6, 2, 6, incident=True)
            X_145 = eval_trilinear_point(model, A, B, C, 'b*c*(3*a - b - c)', ID="X_145", classes=["center", "incident"])
            X_190 = eval_trilinear_point(model, A, B, C, 'b*c/(b - c)', ID="X_190", classes=["center", "incident"])
            central_line(model, X_145, X_190, 145, 190, incident=True)
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_542 = eval_barycentric_point(model, A, B, C, '2*a**(6) - 2*a**(4)*(b**(2) + c**(2)) + a**(2)*(b**(4) + c**(4)) - (b**(2) - c**(2))**(2)*(b**(2) + c**(2))', ID="X_542", classes=["center", "incident"])
            central_line(model, X_4, X_542, 4, 542, incident=True)
            return promote_point_to_top(model, X_1992)


        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_1992 on the given reference triangle."""
            model = create_model('X_1992 = ORTHOCORRESPONDENT OF X_2')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01992(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-01992.json"))
            write_center_svg(
                model_acute,
                here / "x-01992.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1992¶

X₁₉₉₂¶