The Challenge: Al and Curt live at opposite corners of a square lot; Beth and Dawn live at the other two corners. They all carry water from a spring S located within the lot. The spring is 50 feet from Al, 30 feet from Beth, and 40 feet from Curt. How far is the spring from Dawn?
Solution by Lisa Tian, Plymouth-Canton Educational Park
From the Pythagorean theorem, we know 
and
.
Therefore 
.
Also solved by: Phuc Ngo (Jackson H.S.); Oliver Chen, Eileen Chiu, Swaroop Hebbale (Troy Athens H.S.); Sunil Agarwal, Sushil Gupta, Hannah Zhou (Troy H.S.); Katelyn Evans, Thomas Fields, Shannon Higley, Wen Fei Liu, Elise Miller (Forest Hills Northern H.S.); Myron Chang, Catherine Huang, Shelly Jiang, David Kong, Eric Zech (Plymouth-Canton Educational Park); Joe Pawlowski (Grosse Pointe South H.S.); Kyle Martin (Williamston H.S.); Doug Dobney (Marysville H.S.); David Zhang (Ann Arbor Huron); Zachary Noble, Kentaro Mitzushima (Walled Lake Central H.S.). Approximate solutions were submitted by Lea Wojciechowski (Troy Athens H.S.) and Kelly Rickert (Benzie Central H.S.).