Find ∠PRB. Given

I. ∠BPQ = 22^{∘} and O is the centre of the circle

II. ∠RBP = 54^{∘} and chord PQ is parallel to AB

- Either I or II individually is sufficient
- Both I and II together are required
- One of the statements alone is sufficient
- Need more data

Statement I

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…

Statement II

∠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"**