IMC 2009 Q7
7. 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 \(T\)?
- A \(\dfrac{1}{2}\)
- B \(\dfrac{1}{2}\sqrt{2}\)
- C 1
- D \(\sqrt{2}\)
- E 2
Intermediate Mathematical Challenge 2009, Question 7. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: C 1
As can be seen from the diagram, the square whose vertices are the centres of the original four circles has side of length 2 units and this distance is equal to the diameter of the circle through \(X\), \(Y\), \(Z\) and \(T\).
Solution © UK Mathematics Trust, from the IMC 2009 solutions.