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X₈₇₇¶

INTERSECTION OF LINES X₄X_69 AND X₉₉X_112

Let T₁ be the tangential triangle of hyperbola {A, B, C,X₉₉,PU(37)}}. Let T₂ be the tangential triangle of hyperbola {A, B, C,X₄,X₁₁₂,PU(39)}}. Let A'B'C' be the vertex triangle of T₁ and T₂. The lines AA', BB', CC' concur in X₈₇₇. (Randy Hutson, December 29, 2015)

X₈₇₇ (INTERSECTION OF LINES X₄X_69 AND X₉₉X_112) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_877 = INTERSECTION OF LINES X_4X_69 AND X_99X_112."""

        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,
            intersect_lines,
            orthocenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00877(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_877 = INTERSECTION OF LINES X_4X_69 AND X_99X_112 on reference triangle ABC."""
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center"])
            X_69 = eval_trilinear_point(model, A, B, C, '(cos(A))/a**(2)', ID="X_69", classes=["center"])
            X_99 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(2) - c**(2))', ID="X_99", classes=["center"])
            X_112 = eval_trilinear_point(model, A, B, C, 'a/(sin(2*B) - sin(2*C))', ID="X_112", classes=["center"])
            central_line(model, X_4, X_69, 4, 69)
            central_line(model, X_99, X_112, 99, 112)
            X_877 = intersect_lines(model, X_4, X_69, X_99, X_112, ID="X_877", classes=["selected", "target"])
            return promote_point_to_top(model, X_877)


        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_877 on the given reference triangle."""
            model = create_model('X_877 = INTERSECTION OF LINES X_4X_69 AND X_99X_112')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00877(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-00877.json"))
            write_center_svg(
                model_acute,
                here / "x-00877.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X877¶

X₈₇₇¶