USAJMO 2026 Question 6

Emily has a red sheet of paper. She draws $2026$ circles, not necessarily of equal size, colors one circle black, and cuts around all $2026$ circumferences. She separates the paper into at least $2$ black pieces and some red pieces. Is it possible that all the black pieces are congruent?

Proposed by Carl Schildkraut.

Manual essay; 1 editorial point, not official contest scoring.