Students will learn what the Stewart's theorem is, and how to prove it.
How To Prove Stewart's Theorem by MindBoggleTV
2005 AMC 8, Problem 2: Karl bought five folders from Pay-A-Lot at a cost of $2.50 each. Pay-A-Lot had a 20%-off sale the following day. How much could Karl have saved on the purchase by waiting a day.
Here's the solution: The cost of each folder is $2.50. 20% = 1/5. Thus, at 20% off, you can purchase 5 folders for the price of 4. Hence, Karl would have saved $2.50, the cost of 1 folder. Additional, more tedious solutions can be found here.
Mentally determine what fraction is shaded.
Answer: \((1/8)\pi - (1/4)\)