The center of a circle passing through the points and touching the circle is
Explanation for the correct option:
Finding the center of the circle:
The general equation of the circle is with center and radius
Circle passes through the point .
So, substitute and in .
Similarly, Circle passes through the point .
So, substitute and in
.
Now the circle touches another circle with equation .
Since the center of the this circle lies on the circle , the radius of a new circle is equal to the diameter of the circle .
Hence the centres of circle is .
Therefore, the correct answer is option (D).