QQuestion
In the given diagram, RT is a tangent touching the circle at S. If ∠PST = 30° and ∠SPQ = 60°, then ∠PSQ is equal to:
(a) 40°
(b) 30°
(c) 60°
(d) 90°
ICSEClass 10MathematicsCircles01 Mark2023 Moderate
✓Answer
(d) 90°
Explanation:
The angle between a tangent and chord at the point of contact equals the angle in the alternate segment.
Therefore, ∠PQS = ∠PST = 30°.
In triangle PQS:
∠PQS + ∠QPS + ∠PSQ = 180°
30° + 60° + ∠PSQ = 180°
Therefore, ∠PSQ = 90°.
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