How many circles are there in the adjoining figure.

Concept: When circles overlap in a figure, do not try to trace boundaries by eye — mark the centre of every circle you can identify and count only the distinct centres. Each centre corresponds to exactly one complete circle, whether it sits alone or is heavily overlapped by its neighbours, so a systematic labelling of every centre (row by row, or ring by ring) guarantees every circle is counted exactly once, with none skipped and none double-counted.

Application: Marking the centre of every circle in the given figure and numbering them in order gives the labelled figure below.

Reading the numbered figure row by row from top to bottom: the top edge holds 2 circles (8, 9), the widest band beneath it holds 5 circles (13, 2, 3, 4, 10), the next band holds 3 circles (7, 1, 5), and the bottom edge holds 3 more circles (12, 6, 11) — thirteen distinct, complete circles in all, each with its own centre and none formed merely by two circles overlapping.

Cross-check: Summing the count row by row independently of the labelling:

• Top row: 2 circles

• Upper-middle row: 5 circles

• Lower-middle row: 3 circles

• Bottom row: 3 circles

Total = 2 + 5 + 3 + 3 = 13, which matches the count obtained from numbering the centres — confirming there are 13 circles in the given figure, so option (13) is correct.