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WAEC Mathematics 2011 Question 4

Question 4

Circle Theorems

The diagram shows a cyclic quadrilateral PQRS with its diagonals intersecting at K. Which of the following triangles is similar to triangle QKR?

Diagram for this question
  1. A.ΔPQK
  2. B.ΔPKS
  3. C.ΔSKR
  4. D.ΔPSR
Show the answer and explanation

Answer: B (ΔPKS)

Explanation

∠QKR = ∠PKS (vertically opposite) and ∠KQR = ∠SQR = ∠SPR = ∠KPS (angles in the same segment). So ΔQKR ~ ΔPKS.