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.

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
C

Let P and Q be points 2 inches apart, and let A be the area, in square inches, of a circle that passes through P and Q. Which of the following is the set of all possible values of A?
(A)\(0 < A\) (B)\(0 < A \leq \pi\) (C)\(A = \pi\) (D)\(A > \pi\) (E)\(A \geq \pi\)
E

Points E and F lie in the xy-coordinate plane at (0,10) and (6,0), respectively. Which of the following is the midpoint of \(\overline { EF } \) ?
(A)(5,3) (B)(3,5) (C)(3,10) (D)(10,3) (E)(6,10)

B