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Contact Circles

Stage: 3 Short Challenge Level: Challenge Level:1

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.
View the archive of all weekly problems grouped by curriculum topic