The diagram shows 12 small circles of radius 1 and a large circle, inside a square.

Each side of the square is a tangent to the large circle and four of the small circles.

Each small circle touches two other circles.

What is the length of each side of the square?

The answer is 18

**CONTEXT:**

This question came up in a Team Maths Challenge I did back in November. No one on our team knew how to do it and we ended up guessing the answer (please understand that time was scarce and we did several other questions without guessing!) I just remembered this question and thought I'd have a go but I am still struggling with it.

There are no worked solutions online (only the answer) so I reaching out to this website as a final resort. Any help would be greatly appreciated. Thank you!