WAEC Mathematics 2011 Paper

Concept:Intersecting diagonals of a cyclic quadrilateral form triangles that are similar by equal vertically opposite angles and equal angles in the same segment.Explanation:In $\triangle QKR$ and $\triangle PKS$:$\angle QKR = \angle PKS$ because they are vertically opposite angles formed by the intersecting diagonals $PR$ and $QS$.Also, $\angle KRQ = \angle PRQ$ and $\angle KSP = \angle QSP$, since $K$ lies on $PR$ and $QS$.But $\angle PRQ = \angle QSP$, because both are angles in the same segment subtending chord $PQ$.Therefore, $\angle KRQ = \angle KSP$.Hence, $\triangle QKR$ and $\triangle PKS$ are similar by AA similarity.Answer:B. $\triangle PKS$