Contact Circles

These four touching circles have another circle hiding amongst them...
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem

Image
Contact Circles



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.