Mathematics
The given figure shows a circle with center O. If length of arc AQC is double of arc APB and ∠AOB = 65°; then angle AOC is :
65°
2 x 65°
X 65°
none of these
Circles
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Answer
Given, length of arc AQC is double of arc APB.
If arc AQC is twice the length of arc APB, then the angle subtended by arc AQC at the center (∠AOC) will also be twice the angle subtended by arc APB (∠AOB).
∴ ∠AOC = 2 x ∠AOB.
⇒ ∠AOC = 2 x 65°
⇒ ∠AOC = 130°.
Hence, option 2 is the correct option.
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