← etc / Encyclopedia of Triangle Centers

X₁₃₆₆¶

BRISSE TRANSFORM OF X₁₁₁

X₁₃₆₆ (BRISSE TRANSFORM OF X₁₁₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1366 = BRISSE TRANSFORM OF X_111."""

        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_trilinear_point,
            gergonne_point_of,
            intersect_lines,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01366(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1366 = BRISSE TRANSFORM OF X_111 on reference triangle ABC."""
            X_7 = gergonne_point_of(model, A, B, C, ID="X_7", classes=["center"])
            X_1365 = point_from_barycentrics(model, A, B, C, 0.14334182, 0.65139949, 0.20525869, ID="X_1365", classes=["center"])
            X_553 = eval_trilinear_point(model, A, B, C, 'b*c*(2*a + b + c)/(b + c - a)', ID="X_553", classes=["center"])
            X_1358 = eval_trilinear_point(model, A, B, C, '(tan(A/2))**(2)*(sin(B/2 - C/2))**(2)', ID="X_1358", classes=["center"])
            central_line(model, X_7, X_1365, 7, 1365)
            central_line(model, X_553, X_1358, 553, 1358)
            X_1366 = intersect_lines(model, X_7, X_1365, X_553, X_1358, ID="X_1366", classes=["selected", "target"])
            X_222 = eval_trilinear_point(model, A, B, C, 'cos(A)*tan(A/2)', ID="X_222", classes=["center", "incident"])
            X_1367 = point_from_barycentrics(model, A, B, C, 0.34721271, 0.6328996, 0.019887687, ID="X_1367", classes=["center", "incident"])
            central_line(model, X_222, X_1367, 222, 1367, incident=True)
            return promote_point_to_top(model, X_1366)


        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_1366 on the given reference triangle."""
            model = create_model('X_1366 = BRISSE TRANSFORM OF X_111')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01366(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-01366.json"))
            write_center_svg(
                model_acute,
                here / "x-01366.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1366¶

X₁₃₆₆¶