← etc / Encyclopedia of Triangle Centers

X₁₄₉₅¶

CROSSSUM OF X₂ AND X₃₀

X₁₄₉₅ = midpoint of X₂₃ and X₁₁₀

X₁₄₉₅ (CROSSSUM OF X₂ AND X₃₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1495 = CROSSSUM OF X_2 AND X_30."""

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


        def construct_x_01495(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1495 = CROSSSUM OF X_2 AND X_30 on reference triangle ABC."""
            X_23 = eval_trilinear_point(model, A, B, C, 'a*(b**(4) + c**(4) - a**(4) - b**(2)*c**(2))', ID="X_23", classes=["center"])
            X_110 = eval_trilinear_point(model, A, B, C, 'csc(B - C)', ID="X_110", classes=["center"])
            X_1495 = midpoint(model, X_23, X_110, ID="X_1495", classes=["selected", "target"], guide=False)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_25 = eval_trilinear_point(model, A, B, C, 'sin(A)*tan(A)', ID="X_25", classes=["center", "incident"])
            central_line(model, X_6, X_25, 6, 25, incident=True)
            central_line(model, X_23, X_110, 23, 110, incident=True)
            X_30 = eval_trilinear_point(model, A, B, C, 'cos(A) - 2*cos(B)*cos(C)', ID="X_30", classes=["center", "incident"])
            X_113 = eval_trilinear_point(model, A, B, C, 'sin(B)*sin(C)*((sin(C))/(cos(C) - 2*cos(A)*cos(B)) + (sin(B))/(cos(B) - 2*cos(A)*cos(C)))', ID="X_113", classes=["center", "incident"])
            central_line(model, X_30, X_113, 30, 113, incident=True)
            return promote_point_to_top(model, X_1495)


        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_1495 on the given reference triangle."""
            model = create_model('X_1495 = CROSSSUM OF X_2 AND X_30')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01495(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-01495.json"))
            write_center_svg(
                model_acute,
                here / "x-01495.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1495¶

X₁₄₉₅¶