This image contains several geometry problems written in Russian. Let me summarize the key points and provide help with each problem.

1. Triangle ABC is similar to triangle A₁B₁C₁, where BD and B₁D₁ are medians and AD is 3 times larger than AD₁. Find the ratio of the perimeters of triangles ABC and A₁B₁C₁.

2. In triangle ABC, the altitudes AF and CE are drawn. Which of the following statements is correct regarding the altitudes?

   • 1. Triangle EBC is similar to triangle FBA
   • 2. Triangle AFC is similar to triangle CEA
   • 3. Triangle ABC is similar to triangle AOC
   • 4. Triangle AEO is similar to triangle CFO

3. In a right triangle ABC with ∠C = 90°, AC = 6 cm, AB = 9 cm, and CD is the altitude, find BD.

   • a) 8 cm
   • b) 6 cm
   • c) 4 cm
   • d) 5 cm

4. The altitudes of a parallelogram are 6 dm and 10 dm, and the perimeter of the parallelogram is 48 dm. Find the difference between the lengths of adjacent sides of the parallelogram.

   • a) 5 dm
   • b) 4 dm
   • c) 6 dm
   • d) 3 dm

5. In triangle MKP, MP = 24 cm, and DE || MP, segments DE and MK intersect at points D and E. Find MK if DM = 6 cm and DE = 20 cm.

   • a) 32 cm
   • b) 25 cm
   • c) 86 cm
   • d) 24 cm

Would you like to focus on solving any of these problems? Let me know if you need detailed solutions!