SSC CGL 6 Aug 2017 Shift 1 Paper

Question : 73 of 100

Marks: +1, -0

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 5 such that QS =OR. If ∠QSR =30°, then what is the value (in degrees) of POR ?

Validate

Solution:

According to the question,

∵ OR = OQ = QS
∴ ∠QOS =∠QSO =30°
In ΔQSO,
∠OQS

= 180° - 30° -3 0 ° = 120°

and ∠PQO +∠OQS = 180°
∠PQO = 180°-120° = 60°
In ΔPOQ, OP=OQ (radius)
∴ ∠OPQ = ∠PQO = 60°
⇒ ∠POQ = 60°
and
∠POR + ∠POQ + ∠QOS = 180°
⇒ ∠POR + 60°+30° = 180°
∴ ∠POR = 180°-90° = 90°

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