The question is from the topic circles. It is a data sufficiency question. Finding the angle subtended by a chord at the centre would help. CAT Geometry questions are heavily tested in CAT exam. Make sure you master Geometry problems.
Question 32: Find ∠PRB. Given
I. ∠BPQ = 22∘ and O is the centre of the circle
II. ∠RBP = 54∘ and chord PQ is parallel to AB
O is the centre implies AB is the diameter
∠BPQ = 22∘
Let us join OP and see what we get.
OP = OB
∠OPB = ∠OBP (Triangle OPB is isosceles)
If only we know ∠POB, then we can find the answer…
∠RBP = 54∘
Chord PQ is parallel to AB implies ∠BPQ = ∠ABP
We definitely need one of the above angle to get some clue…
Let us combine both the statements
Since ∠BPQ = 22∘, ∠ABP = 22∘
∠POB = 180 – (22 + 22) = 136
∠PRB is nothing but the angle subtended by the chord PB and is half the angle at the center.
∠PRB = ∠POB / 2 = 136/ 2 = 68∘
We need both statements together to arrive at a solution!
The question is "Choose the correct answer"
Choice B is the correct answer.
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