← etc / Encyclopedia of Triangle Centers

X₁₄₉¶

REFLECTION OF X₂₀ IN X₁₀₄

X₁₄₉ is the {X₁₁,X₁₀₀}-harmonic conjugate of X₂. For a list of harmonic conjugates, click Tables at the top of this page.

X₁₄₉ (REFLECTION OF X₂₀ IN X₁₀₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_149 = REFLECTION OF X_20 IN X_104."""

        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_trilinear_point,
            feuerbach_point_of,
            nagel_point_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00149(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_149 = REFLECTION OF X_20 IN X_104 on reference triangle ABC."""
            X_149 = eval_trilinear_point(model, A, B, C, '(b*c*(b**(3) + c**(3) - a**(3) + (a**(2) - b*c)*(b + c) + a*(b*c - b**(2) - c**(2))))', ID="X_149", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_11 = feuerbach_point_of(model, A, B, C, ID="X_11", classes=["center", "incident"])
            central_line(model, X_2, X_11, 2, 11, incident=True)
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center", "incident"])
            X_80 = eval_trilinear_point(model, A, B, C, '1/(1 - 2*cos(A))', ID="X_80", classes=["center", "incident"])
            central_line(model, X_8, X_80, 8, 80, incident=True)
            X_20 = eval_trilinear_point(model, A, B, C, 'cos(A) - cos(B)*cos(C)', ID="X_20", classes=["center", "incident"])
            X_104 = eval_trilinear_point(model, A, B, C, '1/(-1 + cos(B) + cos(C))', ID="X_104", classes=["center", "incident"])
            central_line(model, X_20, X_104, 20, 104, incident=True)
            return promote_point_to_top(model, X_149)


        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_149 on the given reference triangle."""
            model = create_model('X_149 = REFLECTION OF X_20 IN X_104')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00149(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-00149.json"))
            write_center_svg(
                model_acute,
                here / "x-00149.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X149¶

X₁₄₉¶