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Question

Assertion (A) In the given figure, If O is the centre of the circle and AC is the diameter with APB=120, then BQC=150.

Reason (R) In a cyclic quadrilateral, the sum of opposite angles is 180.
which of the following is true?

A
(A) is true and (R) is the correct explanation of (A)
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B
(A) is false and (R) is the correct explanation of (A)
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C
(A) is true and (R) is false
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D
Both (A) and (R) are false
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Solution

The correct option is A (A) is true and (R) is the correct explanation of (A)
Given, APB=120

In cyclic quadrilateral ACBP,
APB+ACB=180120+ACB=180ACB=60
Also, ABC=90 [angle in a semi circle]
InΔABC,BAC+BCA+ABC=180BAC+60+90=180BAC=30
Again, in cyclic quadrilateral ACQB,
CAB+CQB=18030+CQB=180CQB=150
Reason (R)True

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