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X₃₀₆₃¶

CROSSDIFFERENCE OF X₇ AND X₈

X₃₀₆₃ is the perspector of the triangle ABC and the tangential triangle of the conic that passes through the points A, B, C, X₅₅, and X₅₆.

X₃₀₆₃ (CROSSDIFFERENCE OF X₇ AND X₈) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3063 = CROSSDIFFERENCE OF X_7 AND X_8."""

        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,
            cevapoint,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            point_from_barycentrics,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03063(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3063 = CROSSDIFFERENCE OF X_7 AND X_8 on reference triangle ABC."""
            X_798 = eval_trilinear_point(model, A, B, C, 'a**(2)*(b**(2) - c**(2))', ID="X_798", classes=["center"])
            X_3049 = eval_trilinear_point(model, A, B, C, 'a**(2)*(b*sin(A - B) - c*sin(A - C))', ID="X_3049", classes=["center"])
            X_3063 = cevapoint(model, A, B, C, X_798, X_3049, ID="X_3063", classes=["selected", "target"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_513 = eval_trilinear_point(model, A, B, C, 'b - c', ID="X_513", classes=["center", "incident"])
            central_line(model, X_6, X_513, 6, 513, incident=True)
            X_59 = eval_trilinear_point(model, A, B, C, '1/(1 - cos(B - C))', ID="X_59", classes=["center", "incident"])
            X_919 = point_from_barycentrics(model, A, B, C, -0.11560694, 0.83236994, 0.28323699, ID="X_919", classes=["center", "incident"])
            central_line(model, X_59, X_919, 59, 919, incident=True)
            X_521 = eval_trilinear_point(model, A, B, C, '(sec(B) - sec(C))*(csc(A))', ID="X_521", classes=["center", "incident"])
            X_650 = eval_trilinear_point(model, A, B, C, 'cos(B) - cos(C)', ID="X_650", classes=["center", "incident"])
            central_line(model, X_521, X_650, 521, 650, incident=True)
            return promote_point_to_top(model, X_3063)


        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_3063 on the given reference triangle."""
            model = create_model('X_3063 = CROSSDIFFERENCE OF X_7 AND X_8')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03063(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-03063.json"))
            write_center_svg(
                model_acute,
                here / "x-03063.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3063¶

X₃₀₆₃¶