← etc / Encyclopedia of Triangle Centers

X₃₆₂₂¶

H(X₈; M,-1/2)

X₃₆₂₂ = {X₁,X₂}-harmonic conjugate of X₁₄₅

X₃₆₂₂ (H(X₈; M,-1/2)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3622 = H(X_8; M,-1/2)."""

        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_trilinear_point,
            incenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03622(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3622 = H(X_8; M,-1/2) on reference triangle ABC."""
            X_3622 = eval_trilinear_point(model, A, B, C, '2*r + R*sin(B)*sin(C)', ID="X_3622", 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_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=["center", "incident"])
            X_377 = eval_trilinear_point(model, A, B, C, '(b*c*(b**(4) + c**(4) - a**(4) - 2*b**(2)*c**(2) - 2*a*b*c*(a + b + c)))', ID="X_377", classes=["center", "incident"])
            central_line(model, X_149, X_377, 149, 377, incident=True)
            X_21 = eval_trilinear_point(model, A, B, C, '1/(cos(B) + cos(C))', ID="X_21", classes=["center", "incident"])
            X_999 = eval_trilinear_point(model, A, B, C, '2 - cos(A)', ID="X_999", classes=["center", "incident"])
            central_line(model, X_21, X_999, 21, 999, incident=True)
            return promote_point_to_top(model, X_3622)


        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_3622 on the given reference triangle."""
            model = create_model('X_3622 = H(X_8; M,-1/2)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03622(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-03622.json"))
            write_center_svg(
                model_acute,
                here / "x-03622.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3622¶

X₃₆₂₂¶