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Contact Circles

Age 14 to 16 Short Challenge Level:



Four touching circles all have radius 1 and their centres are at the corners of a square.

What is the radius of the circle through the points of contact $X, Y, Z$ and $T$?
 



If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

 

 

 

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.