A is sufficient
Statement A : It is given that the center of the circle is 0 (0,0) & 1 end point of the Chord AB A (8,6). Further AB is parallel to the Y - Axis. From the above we can form the triangle AOB with height of 6 & base of 8. Using Pytha theorem we can find the Hypoth OA which is the radius. From this it is possible to find the coordinates of B using Pythag theorem
Statement B : From the eqn of circle we can only compute the radius of circle which is 10 & thus is insufficient
Hope this helps
Why do you need to use the pythagorean theorem. Its pretty simple as it is. 8,6 means one half is 6 units long since it is parallel to y axis. Just double (since the circle is centered at origin) 6*2=12
which is the length of the cord. Had it not been parallel to the y-axis, it was a whole different story altogether and pythagorean theorem could have come in.
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