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.

Points Q, R, and S lie on \(\overline { XZ } \) in such a way that Q is the midpoint of \(\overline { XZ } \), R is the midpoint of \(\overline { XQ } \) and S is the mid point of \(\overline { QZ } \). If QS = 4, what is length of RZ?
(A)8 (B)12 (C)16 (D)20 (E)24
B

Points J, K, and L lie on a circle whose center is point O. If \(\overline {JK}\) passes through O, which of the following is true about triangle LOK?
(A)All three angles are less then 90 degrees. (B)One angle measures exactly 90 degrees. (C)At least one angle is greater than 90 degrees. (D)At least two of the angles have the same measure. (E)\(\overline {KO} = \overline{KL}\)
D

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)\(\frac { 4 } { 3 } \)

A