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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