In the figure QR is a common tangentogiven circles which meets the tangentTP at P. If QP = 3.8 cm, the length o1QR is

To solve the problem, we will follow the steps outlined:

1. Break Down the Problem

We need to find the length of the tangent QR that meets other points in the configuration of the circles and tangents. The only given measurement is $QP = 3.8$ cm.

2. Relevant Concepts

We will use the property of tangents from a common external point to two circles, which states that the lengths of the tangents drawn from an external point to the points of tangency to the circles are equal.

3. Analysis and Detail

Since the length $QP$ is given as $3.8$ cm and assuming that $QR$ is also a tangent from point Q to a circle around point R, the length of the tangent $QR$ can be calculated if we have further information about the configuration.

However, in many cases where circles are involved, the length of the common tangent can be expressed as $QR = \sqrt{PQ^2 - r_1 \times r_2}$ where $r_1$ and $r_2$ are the radii of the circles.

But, since the specific radii and other configurations are not given, we may conclude that:

4. Verify and Summarize

Based on typical geometric properties, and unless further information is provided about the radius or other distances, if we assume simple geometry where $QR$ can be approximated from $QP$, we take:

$QR = QP$

Thus,

$QR \approx 3.8 \text{ cm}$

Final Answer

The length of $QR$ is approximately $3.8$ cm.