Given any angle ∠XOY in a plane, a ray OP is said to bisect the angle if ∠XOP=∠POY.
a. (a) Construct a ray OP that bisects ∠XOY.
b. (b) Prove that the two angles formed, ∠XOP and ∠POY, are indeed equal.
c. (c) Demonstrate that no second ray other than OP can divide ∠XOY into two equal parts, thereby establishing the uniqueness of the angle bisector.