← etc / Encyclopedia of Triangle Centers

X₈₈₆¶

INTERSECTION OF LINES X₉₉X_669 AND X₅₁₂X_670

X₈₈₆ (INTERSECTION OF LINES X₉₉X_669 AND X₅₁₂X_670) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_886 = INTERSECTION OF LINES X_99X_669 AND X_512X_670."""

        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,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00886(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_886 = INTERSECTION OF LINES X_99X_669 AND X_512X_670 on reference triangle ABC."""
            X_886 = eval_barycentric_point(model, A, B, C, 'b**(2)*c**(2)/((b**(2) - c**(2))*(a**(2)*b**(2) + a**(2)*c**(2) - 2*b**(2)*c**(2)))', ID="X_886", classes=["selected", "target"])
            X_99 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(2) - c**(2))', ID="X_99", classes=["center", "incident"])
            X_669 = eval_trilinear_point(model, A, B, C, 'a**(3)*(b**(2) - c**(2))', ID="X_669", classes=["center", "incident"])
            central_line(model, X_99, X_669, 99, 669, incident=True)
            X_512 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) - c**(2))', ID="X_512", classes=["center", "incident"])
            X_670 = eval_trilinear_point(model, A, B, C, '1/(a**(3)*(b**(2) - c**(2)))', ID="X_670", classes=["center", "incident"])
            central_line(model, X_512, X_670, 512, 670, incident=True)
            X_880 = point_from_barycentrics(model, A, B, C, 4.3698192, 0.10246315, -3.4722823, ID="X_880", classes=["center", "incident"])
            X_892 = point_from_barycentrics(model, A, B, C, -0.10419811, 0.98771128, 0.11648683, ID="X_892", classes=["center", "incident"])
            central_line(model, X_880, X_892, 880, 892, incident=True)
            return promote_point_to_top(model, X_886)


        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_886 on the given reference triangle."""
            model = create_model('X_886 = INTERSECTION OF LINES X_99X_669 AND X_512X_670')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00886(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-00886.json"))
            write_center_svg(
                model_acute,
                here / "x-00886.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X886¶

X₈₈₆¶