← etc / Encyclopedia of Triangle Centers

X₉₃₃¶

X₄-CROSS CONJUGATE OF X₂₅₀

Let P be a point on the circumcircle, and let

(Oab) = circle through A tangent to line BC at B

(Oac) = circle through A tangent to line BC at C

B_a = point other than A where the line PB meets (Oab)

C_a = point other than A where the line PC meets (Oac)

Hab = orthocenter of APBa

Hac = orthocenter of APCa

X₉₃₃ (X₄-CROSS CONJUGATE OF X₂₅₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_933 = X_4-CROSS CONJUGATE OF X_250."""

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


        def construct_x_00933(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_933 = X_4-CROSS CONJUGATE OF X_250 on reference triangle ABC."""
            X_933 = eval_trilinear_point(model, A, B, C, 'sec(A)*csc(2*B - 2*C)', ID="X_933", classes=["selected", "target"])
            X_54 = eval_trilinear_point(model, A, B, C, 'sec(B - C)', ID="X_54", classes=["center", "incident"])
            X_74 = eval_trilinear_point(model, A, B, C, '1/(cos(A) - 2*cos(B)*cos(C))', ID="X_74", classes=["center", "incident"])
            central_line(model, X_54, X_74, 54, 74, incident=True)
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_137 = point_from_barycentrics(model, A, B, C, 0.1354431, 0.64976082, 0.21479608, ID="X_137", classes=["center", "incident"])
            central_line(model, X_4, X_137, 4, 137, incident=True)
            X_98 = eval_trilinear_point(model, A, B, C, 'sec(A +  omega  )', ID="X_98", classes=["center", "incident"])
            X_275 = eval_trilinear_point(model, A, B, C, 'csc(2*A)*sec(B - C)', ID="X_275", classes=["center", "incident"])
            central_line(model, X_98, X_275, 98, 275, incident=True)
            return promote_point_to_top(model, X_933)


        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_933 on the given reference triangle."""
            model = create_model('X_933 = X_4-CROSS CONJUGATE OF X_250')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00933(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-00933.json"))
            write_center_svg(
                model_acute,
                here / "x-00933.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X933¶

X₉₃₃¶