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Contact Circles

Stage: 3 Short Challenge Level: Challenge Level:1
See all short problems arranged by curriculum topic in the short problems collection



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.