In the diagram, the circumference of the external large circle is
1) longer, or
2) shorter, or
3) equal to,
the sum of the circumferences of all inner circles centered on the common diameter, tangent to each other.
Answer: 3) equal
circumference = π. diameter
Let d be the diameter of the external large circle C
Let dj be the diameter of the inner circle Cj
$latex \displaystyle d = \sum_{j} d_j$
$latex \displaystyle \pi. d = \pi. \sum_{j} d_j= \sum_{j}\pi.d_j$
Circumference of the external circle
= sum of circumferences of all inner circles
Mathtuition88 