The radius of a circle is 20 cm. Three more concentric circles are drawn inside it in such a manner that it is divided into 4 equal parts. Find the radius of the smallest circle ?

Options

A. 5 cm
B. 4 cm
C. 10 cm
D. 8 cm

Answer

To find the radius of the smallest circle when three concentric circles are drawn inside a larger circle with a radius of 20 cm, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We have a large circle with a radius of 20 cm. We need to find the radius of the smallest circle when three more concentric circles are drawn inside it, dividing the area into four equal parts.

2. **Identify the Total Number of Circles**: There are four circles in total: one large circle (radius = 20 cm) and three smaller concentric circles.

3. **Determine the Division of the Radius**: Since the area is divided into four equal parts, the radius of the largest circle (20 cm) will be divided into four equal segments. This means we can find the radius of each smaller circle by dividing the total radius by 4.

4. **Calculate the Radius of Each Circle**:
- The radius of the largest circle is 20 cm.
- To find the radius of the smallest circle, we can denote the radii of the circles as follows:
- Radius of the largest circle (R1) = 20 cm
- Radius of the second circle (R2) = 20 cm × (3/4) = 15 cm
- Radius of the third circle (R3) = 20 cm × (2/4) = 10 cm
- Radius of the smallest circle (R4) = 20 cm × (1/4) = 5 cm

5. **Conclusion**: The radius of the smallest circle is 5 cm.

### Final Answer:
The radius of the smallest circle is **5 cm**.