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.

Example Input: In \(\triangle { ABC } \), \(\overline { AB } = \overline { BC } \) and \(\overline { AB } \perp \overline { BC } \). If \(\overline { BC } = 10\), what is the area of the triangle?
(A)\(10 \sqrt { 2 } \) (B)25 (C)50 (D)\(50 \sqrt { 2 } \) (E)100
Example Output: C

Example Input: If a rectangular rug measures 72 inches by 96 inches, what is its area in square feet? (1 foot = 12 inches)
(A)864 (B)576 (C)336 (D)144 (E)48
Example Output: E

Example 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)
Example Output:
E