In Figure, `O` is the centre of the circle of radius `5\ c mdotO P\ _|_A B ,\ O Q\ _|_C D ,\ A B C D ,\ A B=6\ c m\ a n d\ C D=8\ c mdot` Determine `P Qdot`

Explanation

To solve the problem, we need to determine the length of segment \( PQ \) in the given circle configuration. Here’s a step-by-step solution:

### Step 1: Understand the Problem
We have a circle with center \( O \) and radius \( 5 \) cm. Lines \( AB \) and \( CD \) are parallel, with \( OP \) perpendicular to \( AB \) and \( OQ \) perpendicular to \( CD \). The lengths of \( AB \) and \( CD \) are given as \( 6 \) cm and \( 8 \) cm, respectively.

### Step 2: Determine the Lengths of \( AP \) and \( CQ \)
Since \( OP \) is perpendicular to \( AB \) and bisects it, we can find \( AP \) and \( PB \):
- \( AB = 6 \) cm, so \( AP = PB = \frac{6}{2} = 3 \) cm.
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