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Let C(1) " and" C(2) be the centres of t...

Let `C_(1) " and" C_(2)` be the centres of the circles `x^(2)+y^(2)-2x-2y-2=0 " and" x^(2)+y^(2)-6x-6y+14=0`, respectively. If P and Q are the points of intersection of these circles, then the area (in sq. units) of the quadrilateral `PC_(1)QC_(2)` is

A

8

B

4

C

6

D

9

Text Solution

Verified by Experts

The correct Answer is:
B
Given circles,
`x^(2)+y^(2)-2x-2y-2=0 " "...(i)`
and `x^(2)+y^(2)-6x-6y+14=0" "...(ii)`
are intersecting each other orthogonally, because
2(1)(3)+2(1)(3)=14-2
`[therefore " two circle are intersected orthogonally if "2g_(1)g_(2)+2f_(1)f_(2)=c_(1)+c_(2)]`

So, area of quadrilateral
`PC_(1)QC_(2)=2xxar(DeltaPC_(1)C_(2))`.
`=2xx((1)/(2)xx2xx2)=4` sq units.
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