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:
If a square and an equilateral triangle have equal perimeters, what is the ratio of the area of the triangle to the area of the square?
(A)\(\frac { 4\sqrt { 3 } } { 9 } \) (B)\(\frac { 4 } { 9 } \) (C)\(\frac { 3 } { 4 } \) (D)\(\frac { 1 } { 1 } \) (E)\(\frac { 4 } { 3 } \)
answer:
A


question:
Six lines intersect at one point to form 12 equal angles that are non-overlapping. What is the measure, in degrees, of one of these angles?
(A)15 (B)20 (C)30 (D)45 (E)60
answer:
C


question:
A circle with radius r is inscribed in a square. If a point within the square is randomly selected, what is the probability that the point will not be within the circle?
(A)\(\frac { \pi } { 4 } \) (B)\(\frac { \pi - 4 } { 4 } \) (C)\(\frac { 4 - \pi } { 4 } \) (D)\(\pi r\) (E)\(4r\)
answer:

C