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PQ is the chord of a circle whose centre is O. ROS is a line segment originating from a point R on the circle that intersect PQ produced at point S such that QS = OR. If ∠QSR = 30°, then what is the value (in degrees) of POR?

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PQ is the chord of a circle whose centre is O. ROS is a line segment originating from a point R on the circle that intersect PQ produced at point S such that QS = OR. If ∠QSR = 30°, then what is the value (in degrees) of POR?
1). 30
2). 45
3). 60
4). 90


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4 ) 90.

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Give a circle with centre, O. A chord PQ to produced to S, such that ROS (R, being on the circumference) QS = OR.

QS = OR = OQ = being radii.

In isosceles triangle OQS, QS = OQ, so

 

In isosceles triangle POQ,

 

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