509: Circles 2

Several days ago, I posted a slightly different question about tangential circles and the spaces in between. Compare this question, from the 2004 SAT Practice Test to that question from Emma Bell.

• Which question seems harder? What are the difficult aspects of each?
• Do we have to specify the angle APB?
• How are these two questions different in terms of the knowledge they require for solving?
• Is this question made harder by the "how many times" part? Does that phrasing make the question unnatural?

source: ETS, 2004