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).

“Three circles with the same radius *r* all pass through a point *H*. Prove that the circle passing through the points where the pairs of circles intersect (that is, points *A*, *B*, and *C*) also has the same radius *r*.”

Indeed, I found this quite challenging. It took me several weeks to work out my approach and details.