1
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Question

# In the given figure if O is the centre of the circle, then ∠CAB equals

A

90

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B

75

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C

50

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D

45

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Solution

## The correct option is D 45∘ Given, O is the centre of the circle. Hence AB is the diameter of the given circle. Since angle in the semicircle is 90 degrees, ∠ACB=90∘ Also, given, AC = BC. We know that, in a triangle angles opposite to equal sides are equal. Hence ∠CAB=∠CBA=x∘ (say) Now, by applying angle sum property to triangle ABC, we get ∠ACB+∠CAB+∠CBA=180∘ i.e., 90∘+x∘+x∘=180∘ ⟹x∘=45∘ Therefore ∠CAB=45∘

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