Question
Download Solution PDFFrom an external point A, tangents AP and AQ are drawn to a circle with centre O. If ∠APQ = 40°, then find ∠POQ.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
From an external point A, tangents AP and AQ are drawn to a circle with centre O.
∠APQ = 40º
Concept Used:
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.
Calculation:
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 × 40º
⇒ ∠POQ = 80º
∴ The angle ∠POQ is 80º.
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