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

Options

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)`

Answer

3

Explanation

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)`.