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Two variable chords AB and BC of a circl...

Two variable chords AB and BC of a circle `x^(2)+y^(2)=a^(2)` are such that `AB=BC=a`. M and N are the midpoints of AB and BC, respectively, such that the line joining MN intersects the circles at P and Q, where P is closer to AB and O is the center of the circle.
The locus of the points of intersection of tangents at A and C is

A

`x^(2)+y^(2)=a^(2)`

B

`x^(2)+y^(2)=2a^(2)`

C

`x^(2)+y^(2)=4a^(2)`

D

`x^(2)+y^(2)=8a^(2)`

Text Solution

Verified by Experts

The correct Answer is:
3

The locus of the point of intersection of tangents at A and C is a circle whose center is O(0,0) and radius is
`OT = a cosec. (pi)/(6) =2a`
So, the locus is `x^(2)+y^(2)= 4a^(2)`.
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