This seemingly magical result from Futility Closet defies proof at first. Go to the Wolfram demo by Jay Warendorff and then …
“Grab point B above and drag it to a new location. Surprisingly, M, the midpoint of RS, doesn’t move.
This works for any triangle — draw squares on two of its sides, note their common vertex, and draw a line that connects the vertices of the respective squares that lie opposite that point. Now changing the location of the common vertex does not change the location of the midpoint of the line.
It was discovered by Dutch mathematician Oene Bottema.”
As we shall see, Bottema’s Theorem has shown up in other guises as well.
This is a nice 
This surprising, but simple, puzzle is from the 12 April MathsMonday 
This is a simple problem from Five Hundred Mathematical Challenges:
Here is yet another collection of beautiful geometric problems from Catriona Agg (née Shearer). For some reason I found these a bit more challenging than the previous ones. Some of them required more time to “see” the breakthrough.
This is another Brainteaser from the Quantum math magazine .
These two interesting problems were posed on MEI’s MathsMonday site on 
Here is a problem from the Quantum magazine, only this time from the “Challenges” section (these are expected to be a bit more difficult than the Brainteasers).
This is an interesting problem from the 1977 Canadian Math Society’s magazine, Crux Mathematicorum.
Here is yet another problem from