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In the Figure, O is the Centre of the Circle and the Length of Arc Ab is Twice the Length of Arc Bc. If Angle Aob = 108°, Find: - Mathematics

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Question

In the figure, O is the centre of the circle and the length of arc AB is twice the length of arc BC. If angle AOB = 108°, find : ∠CAB 

Solution


Join AD and DB

Arc B = 2 arc BC and ∠AOB = 180°

∴ ∠BOC = 1 ∠AOB
              = `1/2 xx108°`
              = 54°

Now, Arc BC subtends ∠BOC at the centre and

∠CAB at the remaining part of the circle.

∴ `∠CAB = 1/2 ∠BOC`
               =` 1/2xx  54°`
               = 27°

  Is there an error in this question or solution?
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APPEARS IN

 Selina Solution for Concise Mathematics for Class 10 ICSE (2020 (Latest))
Chapter 17: Circles
Exercise 17(B) | Q: 8.1 | Page no. 265
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In the Figure, O is the Centre of the Circle and the Length of Arc Ab is Twice the Length of Arc Bc. If Angle Aob = 108°, Find: Concept: Arc and Chord Properties - the Angle that an Arc of a Circle Subtends at the Center is Double that Which It Subtends at Any Point on the Remaining Part of the Circle.
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