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Question

Pair of tangents are drawn from a point P on x2+y2=4 to x2+y220x20y+199=0. If A and B are points of contact of these tangents, then the area bounded by the locus of circumcentre of PAB is (in sq. units)

A
π
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B
π
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C
4π
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D
100π
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Solution

The correct option is A π
Let P=(2cosθ,2sinθ)
x2+y220x20y+199=0
Center C=(10,10)


PACB is a cyclic quadrilateral
Circumcircle of PAB has PC as diameter, so the circumcentre (h,k) is midpoint of P and C
(h,k)=(5+cosθ,5+sinθ)
Therefore, the locus is
(h5)2+(k5)2=1(x5)2+(y5)2=1
Hence, the required area =π(1)2=π sq. units

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