Mathematics
In the figure (ii) given below, O is the centre of the circle. PS and PT are tangents and ∠SPT = 84°. Calculate the sizes of the angles TOS and TQS.
Circles
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Answer
Since PS and PT are tangents on the circle. So,
∠OSP = ∠OTP = 90°.
Since, sum of angles in a quadrilateral = 360
∠TOS + ∠OTP + ∠SPT + ∠OSP = 360°
∠TOS + 90° + 84° + 90° = 360°
∠TOS + 264° = 360°
∠TOS = 360° - 264°
∠TOS = 96°.
Reflex ∠TOS = 360° - ∠TOS = 360° - 96° = 264°.
Arc ST subtends reflex ∠TOS at the centre and ∠TQS at the remaining part of the circle.
∴ Reflex ∠TOS = 2∠TQS
∠TQS = x Reflex ∠TOS = x 264° = 132°.
Hence, the value of ∠TOS = 96° and ∠TQS = 132°.
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