To find the length of $PQ$, we can use the information given:

1. We know the radii of the circles:

   • Radius of the circle containing point $Q$: $r = 2.1$ cm.
   • Radius of the circle containing point $P$: $r = 1.2$ cm.
   • Radius of the small circle near $P$: $r = 1.4$ cm.

2. The angle between the line segments connecting the centers of the circles to points $P$ and $Q$ is $106^\circ$.

The approach is as follows:

1. Identify the Distance Between Centers of Circles:

   • Let’s denote:
     • The center of the circle with $r = 2.1$ cm as $O_Q$.
     • The center of the circle with $r = 1.2$ cm as $O_P$.
   • The distance $O_QO_P$ is the sum of the radii of the two larger circles: $O_QO_P = 2.1 + 1.2 = 3.3 \text{ cm}$

2. Apply the Cosine Rule to Find $PQ$:

   • Using the cosine rule in triangle $O_QPQO_P$: [ PQ^2 = O_QO_P^2 + O_QP^2 - 2 \cdot O_QO_P \cdot