This is a nifty problem from Presh Talwalkar.
“This is from a Manga called Q.E.D. I thank Sparky from the Philippines for the suggestion!
A string of beads is formed from 25 circles of the same size. The string passes through the center of each circle. The area enclosed by the string inside each circle is shaded in blue, and the remaining areas of the circles are shaded in orange. What is the value of the orange area minus the blue area? Calculate the area in terms of r, the radius of each circle.”
See the String of Beads Puzzle for solutions.
This is another puzzle from the Maths Masters team, Burkard Polster (aka Mathologer) and Marty Ross as part of their “Summer Quizzes” offerings.
Another 
The Futility Closet website had the following 
Here is another problem from the “Challenges” section of the Quantum magazine.
This is a nice puzzle from the Maths Masters team, Burkard Polster (aka Mathologer) and Marty Ross as part of their “Summer Quizzes” offerings.
This is a nifty 
This is a Catriona Agg problem presented by itself, since it turned out to be the most challenging one I ever tried. Usually I can solve her problems in a few minutes or maybe hours, or sometimes days if they are especially challenging. But this problem has taken me weeks and I had to rely on a non-geometric argument. The problem is full of fascinating and unexpected relationships, but I couldn’t find a way to use them to prove the answer.
Here is yet another (belated) collection of beautiful geometric problems from Catriona Agg (née Shearer).
This is a straight-forward problem from the Scottish Mathematical Council (SMC) Senior Mathematics Challenge.
