since we are given two tangents to the circle , then the centre will lie on their angular bisectors of the two tangents.
the angular bisectors will be x-5=y-7 and x-5=-(y-7).
=> y=x+2 and y=12-x
then the cordinates of the centre can be (x,x+2) and (x,12-x)... putting the values from given options,you can get the centre value.
plz approve my answer..!
priyanka tata