Step 1:You can construct the midpoint M of the line AB. (Draw a circle centred at A, passing through B. Draw a circle centred at B, passing through A. Draw the line connecting the two points where these circles intersect. This line meets AB at M.)

Step 2:Let D be one of the points where the circle C meets the line AB. Draw a circle centred at M, passing through the point D. Let E be the other point where this circle meets the line AB. Then BE=CD. So the circle centred at B, passing through E, is congruent to C.