Question 22

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waecmaths question: 

In the diagram, the tangent MN makes an angle of 55o with the chord PS. If  O is the centre of the circle, find $\angle RPS$

Option A: 

55o

Option B: 

45o

Option C: 

35o

Option D: 

25o

waecmaths solution: 

$\begin{align}  & \angle MSQ={{90}^{\circ }}\text{    }\!\!\{\!\!\text{ tangent to a circle }\!\!\}\!\!\text{ } \\ & \angle PSO=\angle PSQ={{90}^{\circ }}-\angle MSP={{90}^{\circ }}-{{55}^{\circ }}={{35}^{\circ }} \\ & \angle PSO=\angle PSQ={{35}^{\circ }} \\ & \left| SO \right|=\left| PQ \right|\text{   }\!\!\{\!\!\text{ radius of the radius }\!\!\}\!\!\text{ } \\ & \angle PSO=\angle SPO={{35}^{\circ }}\text{ } \\ & \text{ }\!\!\{\!\!\text{ Base angles of an issoceles triangle }\!\!\}\!\!\text{ } \\ & \therefore \angle RPS={{35}^{\circ }} \\\end{align}$

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