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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

Three circles are arranged as shown in the figure. Find the length of PQ given that the radii of the circles are 2.1 cm, 1.2 cm, and 1.4 cm, and the angle between the connecting line segments at P and Q is 106°.

Step-by-step solution to find the length of PQ in a geometric arrangement of three circles with given radii and a known angle. This problem involves the Cosine Rule and circle geometry, making it suitable for high school students in Grades 10-12.

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