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प्रश्न
In the given figure, PA and PB are tangents from external point P to a circle with centre C and Q is any point on the circle. Then the measure of ∠AQB is ______.
पर्याय
`62 (1/2)^circ`
125°
55°
90°
उत्तर
In the given figure, PA and PB are tangents from external point P to a circle with centre C and Q is any point on the circle. Then the measure of ∠AQB is `underlinebb(62 (1/2))^circ`.
Explanation:
Given, ∠APB = 55°
∴ ∠ACB = 180° – 55° = 125° ...`((∵ ∠APB and ∠ACB "are"),("supplementary angles"))`
Now, as we know that
Angle subtended by an arc at the centre = 2 × angle subtended by arc at any point on the remaining part of the circle
∴ 125° = 2 × ∠AQB
`\implies` ∠AQB = `125/2`
= 62.5° or `62 (1/2)^circ`
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