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X₈₂₀¶

CROSSPOINT OF X₁ AND X₂₅₅

X₈₂₀ is the crosspoint of X₁ and X₂₅₅.

X₈₂₀ (CROSSPOINT OF X₁ AND X₂₅₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_820 = CROSSPOINT OF X_1 AND X_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_00820(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_820 = CROSSPOINT OF X_1 AND X_255 on reference triangle ABC."""
            X_820 = eval_trilinear_point(model, A, B, C, '((cos(A))**(2)*((cos(B))**(2) + (cos(C))**(2)))', ID="X_820", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_29 = eval_trilinear_point(model, A, B, C, '(sec(A))/(cos(B) + cos(C))', ID="X_29", classes=["center", "incident"])
            central_line(model, X_1, X_29, 1, 29, incident=True)
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_296 = eval_trilinear_point(model, A, B, C, '(cos(A))/((cos(A))**(2) - cos(B)*cos(C))', ID="X_296", classes=["center", "incident"])
            central_line(model, X_3, X_296, 3, 296, incident=True)
            X_662 = eval_trilinear_point(model, A, B, C, '1/(cot(B) - cot(C))', ID="X_662", classes=["center", "incident"])
            X_775 = eval_trilinear_point(model, A, B, C, '(1/((cos(B))**(2) + (cos(C))**(2)))', ID="X_775", classes=["center", "incident"])
            central_line(model, X_662, X_775, 662, 775, incident=True)
            return promote_point_to_top(model, X_820)


        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_820 on the given reference triangle."""
            model = create_model('X_820 = CROSSPOINT OF X_1 AND X_255')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00820(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-00820.json"))
            write_center_svg(
                model_acute,
                here / "x-00820.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X820¶

X₈₂₀¶