a. Show that the two diagonals drawn from a vertex of a regular pentagon trisect the angle.
b. Since the diagonals trisect the angle, if regular pentagon P Q R S T is folded along the diagonal S P, the side T P will fall on the diagonal P R, as shown on the right. Here T^{\prime} is the position of vertex T after the folding.
Find the ratio \frac{P T^{\prime}}{T^{\prime} R}. Express your answer in the form \frac{a+\sqrt{b}}{c}, where a, b, c are integers.
c. Regular pentagon P Q R S T has an area of 1 square unit. The pentagon is folded along the diagonals S P and R P as shown on the right. Here, T^{\prime} and Q^{\prime} are the positions of vertices T and Q, respectively, after the foldings. The segments S T^{\prime} and R Q^{\prime} intersect at X.Determine the area (in square units) of the uncovered triangle X S R. Express your answer in the form \frac{a+\sqrt{b}}{c}, where a, b, c are integers.
