The image you provided contains math problems related to similar triangles and geometric properties. Here's an overview of the problems presented in the image:

Part I

1. Determining the length of the segment $AB$ based on certain given information.

   • A) 15 dm
   • B) 20 dm
   • C) 25 dm
   • D) 21 dm

2. Given a triangle $ABC$, the problem asks about the length of a side in a specific scenario.

3. Another problem involves calculating the length of a triangle's side with specific geometric conditions.

Part II

6. A quadrilateral $ABCD$ is inscribed in a circle, with various segment relations provided.

7. A geometric problem involving triangles and segment lengths is given, and the user needs to calculate lengths based on certain conditions.

Part III

4. Similar triangles and their properties are examined.

5. A problem related to the diagonals of a quadrilateral is given, with an area calculation involved.

Would you like help with solving any of these problems specifically? Please let me know which one you'd like to focus on, and I can guide you through the solution process.