← etc / Encyclopedia of Triangle Centers

X₆₀₂¶

INTERSECTION OF LINES X₃X_31 AND X₅₆X_255

X₆₀₂ (INTERSECTION OF LINES X₃X_31 AND X₅₆X_255) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_602 = INTERSECTION OF LINES X_3X_31 AND X_56X_255."""

        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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            incenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00602(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_602 = INTERSECTION OF LINES X_3X_31 AND X_56X_255 on reference triangle ABC."""
            X_602 = eval_trilinear_point(model, A, B, C, '(sin(A))**(2) - cos(A)', ID="X_602", classes=["selected", "target"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_31 = eval_trilinear_point(model, A, B, C, 'a**(2)', ID="X_31", classes=["center", "incident"])
            central_line(model, X_3, X_31, 3, 31, incident=True)
            X_36 = eval_trilinear_point(model, A, B, C, '1 - 2*cos(A)', ID="X_36", classes=["center", "incident"])
            X_47 = eval_trilinear_point(model, A, B, C, 'cos(2*A)', ID="X_47", classes=["center", "incident"])
            central_line(model, X_36, X_47, 36, 47, incident=True)
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_201 = eval_trilinear_point(model, A, B, C, '(cos(A))*(1 + cos(B - C))', ID="X_201", classes=["center", "incident"])
            central_line(model, X_1, X_201, 1, 201, incident=True)
            return promote_point_to_top(model, X_602)


        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_602 on the given reference triangle."""
            model = create_model('X_602 = INTERSECTION OF LINES X_3X_31 AND X_56X_255')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00602(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-00602.json"))
            write_center_svg(
                model_acute,
                here / "x-00602.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X602¶

X₆₀₂¶