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If O is the origin and O Pa n dO Q are t...

If `O` is the origin and `O Pa n dO Q` are the tangents from the origin to the circle `x^2+y^2-6x+4y+8-0` , then the circumcenter of triangle `O P Q` is `(3,-2)` (b) `(3/2,-1)` `(3/4,-1/2)` (d) `(-3/2,1)`

A

`(3,-2)`

B

`(3//2,-1)`

C

`(3//4,-1//2)`

D

`(-3//2,1)`

Text Solution

Verified by Experts

The correct Answer is:
2

Clearly, OPCQ is a cyclic quadrilateral. Then the circumcircle of `Delta OPQ ` passes through the point C.
For this circle, OC is diameter. Then the center is the midpoint of OC, which is `(3//2,-1)`.
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