Problem of the Week
Due Wednesday, October 13, 2021 at 5:00 pm via email to jwswift@gmail.com.
The figure shows four circles. The largest circle intersects the other three circles, but none of the smaller circles intersect. The radii of the three smaller circles are 2, 2, and 1. The sum of the three blue areas outside the largest circle is the same as the yellow area that is inside the largest circle but not inside any of the three smaller circles.
What is the radius of the largest circle?
Rules for Problem of the Week
The contest is open to all undergraduates at Northern Arizona University.
Send your submissions or questions to Jim Swift at jwswift@gmail.com by the due date and time. Please include the subject “potw”. You may attach a pdf to the email. Please do not send jpegs, pngs, MS Word documents, etc. There are many free aps to make a pdf with your phone camera. I like Adobe scan. To answer some problems, you don't need a scan. You can use the “TeX for Gmail” extension to get nice equations within email.
The answers should be clearly and logically explained. The goal is to write mathematics, not to to write down the answer and draw a box around it.
If your instructor gives you credit for submissions to problem of the week, please include their name and the class (e.g. Swift, MAT 239).
Problems will be graded on a scale of 1 to 3. A model solution is posted each week. A ladder listing the points earned is posted in the lobby of the Adel Math Building (across from the MAP room). Your name will be printed on the ladder, but no names will be published on the web. Let me know if you want to remain anonymous on the posted ladder.