In figure, BC is a diameter of the circle and ∠BAO = 60º. Then ∠ADC is equal to ______. - Mathematics

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In figure, BC is a diameter of the circle and ∠BAO = 60º. Then ∠ADC is equal to ______.

Options

  • 30º

  • 45º

  • 60º

  • 120º

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Solution

In figure, BC is a diameter of the circle and ∠BAO = 60º. Then ∠ADC is equal to 60º.

Explanation:

Given: BC is a diameter of the circle and ∠BAO = 60º

Now, in triangle OAB,

OA = OB  .....[Radii of the same circle]

So, ∠ABO = ∠BAO  ......[Angle opposite to equal sides are equal]

∠ABO = ∠BAO = 60º  ......[Given]

Now, ∠ADC = ∠ABC = 60º  .....[∠ADC and ∠ABC are angles in the same segment of a circle are equal]

Therefore, ∠ADC = 60º.

  Is there an error in this question or solution?
Chapter 10: Circles - Exercise 10.1 [Page 100]

APPEARS IN

NCERT Exemplar Mathematics Class 9
Chapter 10 Circles
Exercise 10.1 | Q 9 | Page 100

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