We find the length of one side of the regular pentagon first.

Steps:

1. Draw the diameter IH through O.

2. Construct the perpendicular bisector of OH. Let G be the mid-point of OH.

3. OA is the radius which is perpendicular to IH.

4. Use G as centre, GA as radius to draw an arc AJ, cutting IH at J.

5. Use A as centre, AJ as radius to draw an arc BJE cutting the given circumscribing circle at B and E. 

6. Use B as centre, AB as radius to draw an arc AC, cutting the circle IH at C. Use E as centre, AB as radius to draw an arc AD, cutting the circle IH at D.

7. Join ABCDE, the regular pentagon is formed.