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Question

# ABCD is a cyclic quadrilateral whose side AB is a diameter of the circle through A, B, C and D. If ∠ADC=130∘, find ∠BAC.

A
40
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B
50
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C
60
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D
30
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Solution

## The correct option is A 40∘Construction: Join A and C. This forms a right triangle ACB [ angle in a semicircle is 90∘]From the figure, we can say that ∠B=50∘ [opposite angles in a cyclic quadrilateral are supplementary]Consider triangle ACB.∠ACB=90∘ [ angle in a semicircle is 90∘]∠ABC=50∘ ⟹∠BAC=40∘ [angle sum property of a triangle].

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