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X₂₉₇₉¶

CENTROID OF DUAL OF THE ORTHIC TRIANGLE

X₂₉₇₉ is the centroid of dual of the orthic triangle.

X₂₉₇₉ (CENTROID OF DUAL OF THE ORTHIC TRIANGLE) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2979 = CENTROID OF DUAL OF THE ORTHIC TRIANGLE."""

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


        def construct_x_02979(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2979 = CENTROID OF DUAL OF THE ORTHIC TRIANGLE on reference triangle ABC."""
            X_568 = eval_trilinear_point(model, A, B, C, 'a*(3*R**(2)*(b**(2) + c**(2) - a**(2)) + a**(2)*b**(2) + a**(2)*c**(2) - b**(4) - c**(4))', ID="X_568", classes=["center"])
            X_549 = eval_trilinear_point(model, A, B, C, 'cos(B - C) + 4*cos(A)', ID="X_549", classes=["center"])
            X_2979 = reflection_in_point(model, X_568, X_549, ID="X_2979", classes=["selected", "target"], guide=False)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_51 = eval_trilinear_point(model, A, B, C, 'a**(2)*cos(B - C)', ID="X_51", classes=["center", "incident"])
            central_line(model, X_2, X_51, 2, 51, incident=True)
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_54 = eval_trilinear_point(model, A, B, C, 'sec(B - C)', ID="X_54", classes=["center", "incident"])
            central_line(model, X_3, X_54, 3, 54, incident=True)
            X_22 = eval_trilinear_point(model, A, B, C, 'a*(b**(4) + c**(4) - a**(4))', ID="X_22", classes=["center", "incident"])
            X_110 = eval_trilinear_point(model, A, B, C, 'csc(B - C)', ID="X_110", classes=["center", "incident"])
            central_line(model, X_22, X_110, 22, 110, incident=True)
            return promote_point_to_top(model, X_2979)


        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_2979 on the given reference triangle."""
            model = create_model('X_2979 = CENTROID OF DUAL OF THE ORTHIC TRIANGLE')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02979(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-02979.json"))
            write_center_svg(
                model_acute,
                here / "x-02979.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2979¶

X₂₉₇₉¶