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The diagram shows two identical large circles and two identical smaller circles whose centres are at the corners of a square.
The two large circles are touching, and they each touch the two smaller circles.
The radius of the small circles is $1cm$.
What is the radius of the large circles in centimetres?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?
Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.