# CAT Practice : Coordinate Geometry

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Try to find the angle subtended by the chord PB at the center from the given statements!

## Data Sufficiency

Q.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

1. Either I or II individually is sufficient
2. Both I and II together are required
3. One of the statements alone is sufficient
4. Need more data

Choice (B). Both I and II together are required

## Detailed Solution

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!

Correct Answer: (B). Both I and II together are required

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