instruction:
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.
question:
A certain flag has a length that is 2 times its width. What is the width of a flag that has an area of 100?
(A)5 (B)\(5\sqrt { 2 } \) (C)10 (D)\(10\sqrt { 2 } \) (E)20
answer:
B


question:
If lines \(\overline { BC } \) and \(\overline { BD } \) are each perpendicular to line \(\overline { AB } \), which of the following must be true?
(A)\(\overline { AB } \perp \overline { CD } \) (B)\(\overline { AB } \perp \overline { AC } \) (C)\(\overline { AC } \perp \overline { AD } \) (D)\(\overline { AB } \parallel \overline { CD } \) (E)\(\overline { BC } \perp \overline { BD } \)
answer:
A


question:
If the circumference of circle I is equal to the diameter of circle II, what is the ratio of the area of circle II to the area of circle I?
(A)\(\frac { 1 } { \pi^2 } \) (B)\(\sqrt { \pi } \) (C)\(\pi\) (D)\(\pi^2\) (E)\(4\pi^2\)
answer:

D