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प्रश्न
In the given figure, O is the centre of the circle and angle OAB = 55°, then angle ACB is equal to:
विकल्प
55°
35°
70°
30°
MCQ
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उत्तर
35°
Explanation:
From figure,
In △OAB,
OA = OB (Radius of same circle)
We know that,
Angles opposite to equal sides are equal.
∴ ∠OBA = ∠OAB = 55°
By angle sum property of triangle,
⇒ ∠OBA + ∠OAB + ∠AOB = 180°
⇒ 55° + 55° + ∠AOB = 180°
⇒ ∠AOB + 110° = 180°
⇒ ∠AOB = 180° − 110° = 70°
We know that,
The angle which an arc of a circle subtends at the center is double that which it subtends at any point on the remaining part of the circumference.
∴ ∠AOB = 2∠ACB
∠ACB = `(∠AOB)/2 = (70°)/2` = 35°
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