In the given figure, CD is a direct common tangent to two circles intersecting each other at A and B. Then,

It seems that you are referring to a geometry problem involving two intersecting circles and a tangent line. However, since no figure has been provided and the question is incomplete, I'll provide a general approach to solving problems related to direct common tangents to circles.

1. Break Down the Problem

   • Identify the two circles and their respective centers (let's call them $O_1$ and $O_2$).
   • Mark the points where the circles intersect (points A and B).
   • Analyze the properties of the tangent CD.

2. Relevant Concepts

   • The length of the tangent from a point to a circle can be found using the formula: $\text{Length} = \sqrt{d^2 - r^2}$ where $d$ is the distance from the external point to the center of the circle, and $r$ is the radius of the circle.
   • The properties of the triangles formed by the points and the centers of the circles will also be useful.

3. Analysis and Detail

   • For the tangent line CD, you can derive relationships between the lengths involved and possibly find angles or areas depending on what further information is required.
   • If you are given specific lengths for the radii and the distance between the circle centers, plug those values into the formulas.

4. Verify and Summarize

   • Make sure that any calculations are double-checked.
   • Summarize your findings based on the relationships and any relevant theorems (like the power of a point theorem).

Final Answer

To provide a specific answer, more information is needed regarding the positions of the circles, their radii, or specific lengths related to the tangent line. Please provide any additional details or confirm what you're asking for!