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:
\(A\) (5, 1) lies on a circle whose center is \(O\) (1, 5). If \(AB\) is a diameter, what are the coordinates of \(B\) ?
(A)(3, 3) (B)(6, 6) (C)(-1, 5) (D)(-1, 10) (E)(-3, 9)

Ex Output:
E


Ex Input:
Both \(\triangle { ABC } \) and \(\triangle { AED } \) are equilateral. If \(AD = \frac { 2 } { 3 } DC\), then the perimeter of \(\triangle { AED } \) is what fraction of the perimeter of \(\triangle { ABC } \)?
(A)\(\frac { 1 } { 3 } \) (B)\(\frac { 2 } { 5 } \) (C)\(\frac { 3 } { 5 } \) (D)\(\frac { 2 } { 3 } \) (E)\(\frac { 4 } { 5 } \)

Ex Output:
B


Ex Input:
A rectangle is twice as long as it is wide. If the width is a, what is the length of a diagonal?
(A)\(a\sqrt { 2 } \) (B)\(a\sqrt { 3 } \) (C)\(a\sqrt { 5 } \) (D)\(3a\) (E)\(5a\)

Ex Output:

C