Let the co-ordinates of A and B be (0,0) and (a,0) respectively. Let the co-ordinates of point C be (h, k). Given: 2AC = BC ⇒2√h2+k2=√(h−a)2+k2 ⇒4(h2+k2)=(h−a)2+k2 ⇒4h2+4k2=h2+k2+a2−2ah ⇒h2+k2+
2a
3
h−
a2
3
=0 ⇒(h+
a
3
)2+k2=(
2a
3
)2 The equation written above is that of a circle with center (say O) at (−