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Mathematics

In the given figure, O is the centre of the circle and ∠AOB = 150°. Then, ∠ACB = ?

  1. 75°

  2. 105°

  3. 85°

  4. 115°

In the given figure, O is the centre of the circle and ∠AOB = 150°. Loci, RSA Mathematics Solutions ICSE Class 10.

Circles

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Answer

We know that,

The angle which an arc subtends at the center is double that which it subtends at any point on the remaining part of the circumference.

∴ ∠ACB = 12\dfrac{1}{2} Reflex∠AOB

= 3601502\dfrac{360^{\circ} - 150^{\circ}}{2} = 105°.

Hence, option 2 is the correct option.

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