**Given Information:**

- Triangle ABC
- AD is perpendicular to BC
- OB is the angle bisector of angle B
- Angle B = 20 degrees
- Angle DAC = 40 degrees

**To Find:**

- Angle OCD

**Solution:**

To find angle OCD, we need to use the given information and some properties of triangles and angles.

**Step 1: Angle BOC**

Since OB is the angle bisector of angle B, we know that angle BOC = (1/2) * angle B = (1/2) * 20 = 10 degrees.

**Step 2: Angle A**

In triangle ABC, we have angle B + angle A + angle C = 180 degrees (sum of angles in a triangle).

We know that angle B = 20 degrees. Let's say angle A = x degrees. Then, angle C = 180 - (20 + x) = 160 - x degrees.

**Step 3: Angle DAB**

In triangle ABD, we have angle A + angle D + angle B = 180 degrees.

We know that angle A = x degrees, angle B = 20 degrees, and angle D = 90 degrees (since AD is perpendicular to BC).

Substituting these values, we get x + 90 + 20 = 180.

Simplifying, we get x + 110 = 180.

Therefore, x = 180 - 110 = 70 degrees.

**Step 4: Angle DAC**

In triangle DAC, we have angle D + angle A + angle C = 180 degrees.

We know that angle D = 90 degrees, angle A = 70 degrees (from step 3), and angle C = 160 - x = 160 - 70 = 90 degrees.

Substituting these values, we get 90 + 70 + 90 = 180.

Therefore, angle DAC is valid.

**Step 5: Angle OCD**

Since angle DAC = 40 degrees and angle BOC = 10 degrees, angle OCD = angle BOC - angle DAC = 10 - 40 = -30 degrees.

However, angles cannot be negative, so there is no angle OCD in this case.

**Conclusion:**

In the given triangle ABC, with the given conditions, there is no angle OCD.

60′