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.
One example: A ladder is placed against a building such that the top of the ladder forms an angle of 30 degrees with the side of the building. If the ladder is 20 feet long, how far in feet is the bottom of the ladder from the base of the building?
(A)5 (B)10 (C)15 (D)\(20\sqrt{2}\) (E)\(20\sqrt{3}\)
Solution is here: B
Explanation: the ladder makes a right triangle with the wall so the length wanted is sin(30)*20=10

Now, solve this: Points A, B and C are three vertices of a triangle. The location of point X is such that AX = BX. Which of the following could be true? I. X is on \(\overline { AB } \) II. X is inside \(\triangle { ABC } \) III. X is outside \(\triangle { ABC } \)
(A)I only (B)III only (C)I and II only (D)II and III only (E)I, II and III
Solution:
E