PQ is a chord of a circle with centre O and SOR is a line segment originating from a point S on the ...........

Quantitative Aptitude ( CCS) Geometry

PQ is a chord of a circle with centre O and SOR is a line segment originating from a point S on the circle and intersecting PQ produced at R such that QR = OS. If ∠QRO = 30° then ∠POS = ?

70°

90°

60°

80°

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Explanation:

Let radius be 'r' and ∠POS = x°
ΔOQR isoceles ∴∠QOR = 30°
∴ ∠OQR = 120° (Sum of all angles of ΔOQR = 180°)
∴ ∠OQP = 60° (Supplementary agnle)
ΔOPQ isoceles since OP = OQ = r
∴ ∠OQP = 60° = ∠OQP
∴ ∠ POQ = 60° = [Sum of all angle of Δ = 180° ]
Now SOR is a straight line
∴ x + 60° + 30° = 180°
∴ x = 90°