Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two generalizations of the Butterfly Theorem   We establish two direct extensions to the Butterfly Theorem on the cyclic
quadrilateral along with the proofs using the projective method and analytic
geometry of the Cartesian coordinate system.

23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg