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To find the length of \( PQ \) in this problem, we can apply the **Law of Cosines**. Here's the step-by-step solution:

### Step 1: Set Up the Triangle
In this problem:
- We have a triangle \( \triangle PQO \), where \( P \) and \( Q \) are centers of circles with radii 1.4 cm, 1.9 cm, and 1.8 cm respectively.
- The angle \( \angle PQO = 114^\circ \).
- We want to find the distance \( PQ \).

### Step 2: Use the Law of Cosines
The Law of Cosines states:
\[
PQ^2 = (PQO

Three circles are arranged as shown in the figure. Find the length of PQ, given that the radius of circle P is 1.4 cm, the radius of circle Q is 1.8 cm, and the radius of the third circle is 1.9 cm, with the angle between PQ and the third radius being 114°.

Learn how to find the distance PQ between two circle centers using the Law of Cosines. Given radii of 1.4 cm, 1.8 cm, and 1.9 cm, and an angle of 114° between the radius lines, this problem covers key geometry and trigonometry concepts for high school students.

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