Question

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 ______.

Options

• `62 (1/2)^circ`

• 125°

• 55°

• 90°

Answer 1

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`