Question 9

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Jambmaths question: 

P, R and S lies on a circle centre O as shown above, while Q lies outside the circle. Find $\angle$PSO

Option A: 

45o

Option B: 

55o

Option C: 

35o

Option D: 

40o

Jamb Maths Solution: 

$\begin{align}  & \angle PRS=\angle PQR+\angle RPQ\text{   }\!\!\{\!\!\text{ sum of two opp}\text{. interior }\angle \text{sof a }\Delta \text{ }\!\!\}\!\!\text{ } \\ & \angle PRS={{20}^{\circ }}+{{35}^{\circ }}={{55}^{\circ }} \\ & \angle POS=2\times \angle PRS\text{  }\{angle\text{ }at\text{ }centre=\text{ }2\times \angle \text{ }at\text{ }circumference\} \\ & \angle POS=2\times {{55}^{\circ }}={{110}^{\circ }} \\ & PO=OS\text{               }\{radius\text{ }of\text{ }circle\} \\ & \angle OPS=\angle PSO\text{      }\{Base\text{ }angle\text{ }of\text{ }a\text{ }issosceles\text{ }\vartriangle \} \\ & Considering\text{ }\Delta POS \\ & {{110}^{\circ }}+\angle PSO+\angle PSO={{180}^{\circ }} \\ & \angle PSO={{35}^{{}^\circ }} \\\end{align}$

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