The example in the center of the circle shows that our puzzle answers will be interspersed with new words, with the lines connecting instances of the same letter. There are many ways to start and figure out where the words go, but two of the easiest are noting the nine-letter word on the left (with no nine-letter answers) and looking for spaces that will with the two A’s in the word GIVEAWAY.
Once you figure out where to start, the rest of the words easily fall into place. Each of the new words has a missing letter, which must be a specific letter to create the word. The finished puzzle is shown here, with puzzle answers shown in black, new words shown in green, and unchecked letters highlighted in lime.
There are eight marked letters, but the puzzle says that the answer is nine letters long. Fortunately, the puzzle makes a circle, so starting from the word ANALYZES and reading clockwise, the answer EASY AS PIE is spelled out, with the letter E used both at the beginning and the end.