Two circles with centres O and O' of radii 3 cm and 4 cm, respectively intersect at two points P and Q such that OP and O'P are tangents to the two circles. Find the length of common chord PQ.

Explanation

To find the length of the common chord \( PQ \) of two intersecting circles with centers \( O \) and \( O' \) and radii \( 3 \) cm and \( 4 \) cm respectively, we can follow these steps:

### Step 1: Identify the given values
- Radius of circle with center \( O \) (denote as \( r_1 \)) = \( 3 \) cm
- Radius of circle with center \( O' \) (denote as \( r_2 \)) = \( 4 \) cm

### Step 2: Use the Pythagorean theorem
Since \( OP \) and \( O'P \) are tangents to the circles at point \( P \), we can apply the Pythagorean theorem to triangle \( O O'P \).
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