You are given a geometric mathematical question. Questions in this task often involve shapes and Geometric Relationships. You are also given 4 or 5 answer options (associated with "A", "B", "C", "D", "E"). Do not generate anything else apart from one of the following characters: 'A', 'B, 'C', 'D', 'E'. LaTeX mathematical format (the standard way to express mathematical expressions in the typesetting software known as LaTeX) is used to express equations. Each question is solvable with high school math knowledge.

Ex Input:
How many lines can be drawn from one vertex of a cube to the other vertices of the cube, such that the lines are not parallel to any edge of the cube?
(A)4 (B)6 (C)7 (D)24 (E)42

Ex Output:
A


Ex Input:
\begin{gather} x^2 + y^2 + 4x - 2y = -1 \end{gather} The equation of a circle in the xy-plane is shown above. What is the radius of the circle?
(A)2 (B)3 (C)4 (D)9

Ex Output:
A


Ex Input:
If \(A, B, C\), and \(D\) lie on the same straight line, and if \(AC = 2CD = 3BD\), what is the value of the ratio \(\frac { BC } { CD } \)?
(A)\(\frac { 1 } { 6 } \) (B)\(\frac { 1 } { 3 } \) (C)\(\frac { 1 } { 2 } \) (D)\(\frac { 5 } { 3 } \) (E)It cannot be determined from the information given

Ex Output:

E


