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WAEC Mathematics 2009 Question 45

Question 45

Circle Theorems

From the diagram, which of the following statements is/are correct?
I. XQ is a radius of a circle centre Q.
II. |XQ| = |QY|
III. |QX| = |XY|

Diagram for this question
  1. A.I only
  2. B.I and II only
  3. C.II and III only
  4. D.I, II and III.
Show the answer and explanation

Answer: D (I, II and III.)

Explanation

The large arc is drawn with centre Q and radius QX, so I is true and QY = QX (II). The small arc cutting it at Y is drawn from X with the same radius, so XY = QX (III).