GK 2018 Q7
7. The diagram shows a rectangle of size 7 cm × 11 cm containing two circles that each touch three of the sides of the rectangle. What is the distance between the centres of the two circles?
- A 2 cm
- B 2.5 cm
- C 3 cm
- D 3.5 cm
- E 4 cm
Grey Kangaroo 2018, Question 7. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: E 4 cm
From the diagram, it can be seen that the distance between the centres of the two circles is 11 cm – 2 × the radius of a circle or equivalently 11 cm – the diameter of each circle. Since this diameter is 7 cm, the distance between the centres is 11 cm – 7 cm = 4 cm.
Solution © UK Mathematics Trust, from the GK 2018 solutions.