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Q.

Let point P moves in first quadrant while satisfying (given O:(0,0),A:(4,43) and B:(4,0)) (1) It is closer to x-axis than to line OA, and (2) It is closer to origin than to point B,  Then area of the region in which point P can move is greater than or equal to

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a

23

b

3−π4

c

109

d

1

answer is A.

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Detailed Solution

Clearly point P can move in shaded ΔOCD Hence Area of the region=12⋅2⋅2⋅13=23=233≈3.463≈1.15 Clearlyaoptions 1,2,3,4 are all less than 1.15.
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Let point P moves in first quadrant while satisfying (given O:(0,0),A:(4,43) and B:(4,0)) (1) It is closer to x-axis than to line OA, and (2) It is closer to origin than to point B,  Then area of the region in which point P can move is greater than or equal to