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X₂₆¶

CIRCUMCENTER OF THE TANGENTIAL TRIANGLE

Theorems involving X₂₆, published in 1889 by A. Gob, are discussed in

Roger A. Johnson, Advanced Euclidean Geometry, Dover, 1960, 259-260.

X₂₆ (CIRCUMCENTER OF THE TANGENTIAL TRIANGLE) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_26 = CIRCUMCENTER OF THE TANGENTIAL 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,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00026(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_26 = CIRCUMCENTER OF THE TANGENTIAL TRIANGLE on reference triangle ABC."""
            X_26 = eval_trilinear_point(model, A, B, C, 'a*(b**(2)*cos(2*B) + c**(2)*cos(2*C) - a**(2)*cos(2*A))', ID="X_26", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            central_line(model, X_2, X_3, 2, 3)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_143 = eval_trilinear_point(model, A, B, C, '(sec(A))*(cos(2*C - 2*A) + cos(2*A - 2*B))', ID="X_143", classes=["center", "incident"])
            central_line(model, X_6, X_143, 6, 143, incident=True)
            X_68 = eval_trilinear_point(model, A, B, C, 'cos(A)*sec(2*A)', ID="X_68", classes=["center", "incident"])
            X_161 = eval_trilinear_point(model, A, B, C, '(a*((a**(2) + b**(2) + c**(2))*(sin(2*A))**(2) + (c**(2) - b**(2) - a**(2))*(sin(2*B))**(2) + (b**(2) - c**(2) - a**(2))*(sin(2*C))**(2)))', ID="X_161", classes=["center", "incident"])
            central_line(model, X_68, X_161, 68, 161, incident=True)
            return promote_point_to_top(model, X_26)


        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_26 on the given reference triangle."""
            model = create_model('X_26 = CIRCUMCENTER OF THE TANGENTIAL TRIANGLE')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00026(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-00026.json"))
            write_center_svg(
                model_acute,
                here / "x-00026.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X26¶

X₂₆¶