← etc / Encyclopedia of Triangle Centers

X₃₇₀₅¶

X₃₅₅₀com(EXTOUCH TRIANGLE)

X₃₇₀₅ = excentral-to-ABC barycentric image of X₃₅₅₀

X₃₇₀₅ (X₃₅₅₀com(EXTOUCH TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3705 = X_3550com(EXTOUCH 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,
            construct_baseline_triangle,
            create_model,
            eval_barycentric_point,
            eval_trilinear_point,
            feuerbach_point_of,
            incenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03705(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3705 = X_3550com(EXTOUCH TRIANGLE) on reference triangle ABC."""
            X_3705 = eval_barycentric_point(model, A, B, C, '(b**(2)-b*c+c**(2)) * (-a+b+c)', ID="X_3705", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            central_line(model, X_1, X_2, 1, 2, incident=True)
            X_63 = eval_trilinear_point(model, A, B, C, 'cot(A)', ID="X_63", classes=["center", "incident"])
            X_147 = eval_trilinear_point(model, A, B, C, 'b*c*(a**(8) + (b**(2) + c**(2))*a**(6) - (2*b**(4) + 3*b**(2)*c**(2) + 2*c**(4))*a**(4) + (b**(6) + b**(4)*c**(2) + b**(2)*c**(4) + c**(6))*a**(2) - b**(8) + b**(6)*c**(2) + b**(2)*c**(6) - c**(8))', ID="X_147", classes=["center", "incident"])
            central_line(model, X_63, X_147, 63, 147, incident=True)
            X_11 = feuerbach_point_of(model, A, B, C, ID="X_11", classes=["center", "incident"])
            X_312 = eval_trilinear_point(model, A, B, C, '(b + c - a)*b**(2)*c**(2)', ID="X_312", classes=["center", "incident"])
            central_line(model, X_11, X_312, 11, 312, incident=True)
            return promote_point_to_top(model, X_3705)


        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_3705 on the given reference triangle."""
            model = create_model('X_3705 = X_3550com(EXTOUCH TRIANGLE)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03705(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-03705.json"))
            write_center_svg(
                model_acute,
                here / "x-03705.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3705¶

X₃₇₀₅¶