The diagram shows eight circles of two different sizes. The circles are arranged in concentric pairs so that the centres form a square. Each larger circle touches one other larger circle and two smaller circles. The larger circles have radius 1.
What is the exact radius of each smaller circle?
Select one option, then click Submit.
\frac{1}{3}
\frac{2}{5}
\sqrt{2} - 1
\frac{1}{2}
\frac{1}{2}\sqrt{2}
Select an option, then submit.
Sign in or create an account to reveal answers, view the solution, and save your progress. Create a free account to unlock practice and keep track of your work.
Senior Mathematical Challenge 2015 (2015)
One puzzle per day. Cryptarithm, Magic Square, Summit. No sign-up required to play.
Play daily puzzle →Interactive problems and curated lessons—water pouring, magic squares, knight's tour, and more.
Browse library →See how you rank. Top solvers by problems solved correctly. Sign in to climb the ranks.
View leaderboard →Senior Mathematical Challenge 2015 (2015)