← etc / Encyclopedia of Triangle Centers

X₃₈₆₂¶

PERSPECTOR OF ABC AND T(bc, b²)

{X₆₉₄,X₁₅₈₁}-harmonic conjugate of X₃₈₆₃

X₃₈₆₂ (PERSPECTOR OF ABC AND T(bc, b²)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3862 = PERSPECTOR OF ABC AND T(bc, b²)."""

        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,
            construct_baseline_triangle,
            create_model,
            eval_barycentric_point,
            eval_trilinear_point,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03862(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3862 = PERSPECTOR OF ABC AND T(bc, b²) on reference triangle ABC."""
            X_3862 = eval_barycentric_point(model, A, B, C, '(a**(2)*(b**(2) - a*c)*(c**(2) - a*b)*(b**(2) + b*c + c**(2)))', ID="X_3862", classes=["selected", "target"])
            X_75 = eval_trilinear_point(model, A, B, C, '1/a**(2)', ID="X_75", classes=["center", "incident"])
            X_141 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2) + c**(2))', ID="X_141", classes=["center", "incident"])
            central_line(model, X_75, X_141, 75, 141, incident=True)
            X_37 = eval_trilinear_point(model, A, B, C, 'b + c', ID="X_37", classes=["center", "incident"])
            X_256 = eval_trilinear_point(model, A, B, C, '1/(a**(2) + b*c)', ID="X_256", classes=["center", "incident"])
            central_line(model, X_37, X_256, 37, 256, incident=True)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_292 = eval_trilinear_point(model, A, B, C, 'a/(a**(2) - b*c)', ID="X_292", classes=["center", "incident"])
            central_line(model, X_6, X_292, 6, 292, incident=True)
            return promote_point_to_top(model, X_3862)


        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_3862 on the given reference triangle."""
            model = create_model('X_3862 = PERSPECTOR OF ABC AND T(bc, b²)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03862(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-03862.json"))
            write_center_svg(
                model_acute,
                here / "x-03862.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3862¶

X₃₈₆₂¶