IMC 2017 Q2
2. Each of the diagrams below shows a circle and four small squares. In each case, the centre of the circle is the point where all four squares meet.
In one of the diagrams, exactly one third of the circle is shaded. Which one?
Intermediate Mathematical Challenge 2017, Question 2. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: B
When one third of the circle is shaded, the angle at the centre of the shaded sector is 360° ÷ 3 = 120°. In diagram A, the sector angle is 90°. In diagram C, the sector angle is 90° + 90° ÷ 2 = 135°. So the correct diagram has a sector angle greater than that shown in A, but smaller than that shown in C. The only such sector angle is that in B.
Solution © UK Mathematics Trust, from the IMC 2017 solutions. Longer versions with investigations: Solutions and investigations (PDF).