← etc / Encyclopedia of Triangle Centers

X₃₃₁₀¶

BARYCENTRIC PRODUCT X₅₁₃*X₅₁₇

X₃₃₁₀ = crossdifference of every pair of points on the line X₃ X₈

X₃₃₁₀ (BARYCENTRIC PRODUCT X₅₁₃*X₅₁₇) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3310 = BARYCENTRIC PRODUCT X_513*X_517."""

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


        def construct_x_03310(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3310 = BARYCENTRIC PRODUCT X_513*X_517 on reference triangle ABC."""
            X_3310 = eval_trilinear_point(model, A, B, C, '(a*(b - c)*( -1 + cos(B) + cos(C)))', ID="X_3310", classes=["selected", "target"])
            X_230 = eval_trilinear_point(model, A, B, C, 'b*c*(a**(2)*(2*a**(2) - b**(2) - c**(2)) + (b**(2) - c**(2))**(2))', ID="X_230", classes=["center", "incident"])
            X_231 = eval_trilinear_point(model, A, B, C, '(cos(B))*(4*(sin(C))**(2) - 1)*(cos(A)*sin(B) - sin(A)*cos(B)) - (cos(C))*(4*(sin(B))**(2) - 1)*(cos(C)*sin(A) - sin(C)*cos(A))', ID="X_231", classes=["center", "incident"])
            central_line(model, X_230, X_231, 230, 231, incident=True)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_654 = eval_trilinear_point(model, A, B, C, 'cos(A - B) - cos(C - A)', ID="X_654", classes=["center", "incident"])
            central_line(model, X_6, X_654, 6, 654, incident=True)
            X_244 = eval_trilinear_point(model, A, B, C, '(b - c)**(2)', ID="X_244", classes=["center", "incident"])
            X_665 = eval_trilinear_point(model, A, B, C, 'a*((a - b)**(2)*(a + b - c) - (c - a)**(2)*(c + a - b))', ID="X_665", classes=["center", "incident"])
            central_line(model, X_244, X_665, 244, 665, incident=True)
            return promote_point_to_top(model, X_3310)


        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_3310 on the given reference triangle."""
            model = create_model('X_3310 = BARYCENTRIC PRODUCT X_513*X_517')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03310(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-03310.json"))
            write_center_svg(
                model_acute,
                here / "x-03310.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3310¶

X₃₃₁₀¶