From an external point A, tangents AP and AQ are drawn to a circle with center O. If ∠APQ = 40°, then find ∠POQ.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e 80°.
We know that,
The angle between the tangents drawn from an external point to a circle is equal to the angle subtended by the line segment joining the points of contact at the center.
Now,
Let ∠POQ be the angle subtended at the center by the tangents.
We know that the angle between the tangents (∠APQ) is equal to half the angle subtended by the line segment joining the points of contact at the center.
⇒ ∠POQ = 2 × ∠APQ
⇒ ∠POQ = 2 × 40°
⇒ ∠POQ = 80°
Thus, The angle ∠POQ is 80°