O' is the centre of the circle, AB is a chord of the circle, `OM_|_ AB`. If `AB= 20 cm, OM = 2sqrt(11)` cm, then radius of the circle is

Options

A. 15 cm
B. 12 cm
C. 10 cm
D. 11 cm

Answer

To find the radius of the circle given the chord AB and the perpendicular distance OM from the center O to the chord, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Length of chord AB = 20 cm
- OM (perpendicular distance from the center O to the chord AB) = \(2\sqrt{11}\) cm

2. **Determine the Midpoint of the Chord:**
- Since OM is perpendicular to AB, it bisects the chord. Therefore, we can find the lengths of AM and MB.
- Since AB = 20 cm, we have:
\[ AM = MB = \frac{AB}{2} = \frac{20}{2} = 10 \text{ cm} \]

3. **Apply the Pythagorean Theorem:**
- In triangle OMA, we can apply the Pythagorean theorem. Here, OA is the radius (r) of the circle, OM is one leg, and AM is the other leg.
- According to the Pythagorean theorem:
\[ OA^2 = OM^2 + AM^2 \]

4. **Substitute the Values:**
- Substitute OM and AM into the equation:
\[ OA^2 = (2\sqrt{11})^2 + 10^2 \]
- Calculate \(OM^2\) and \(AM^2\):
\[ (2\sqrt{11})^2 = 4 \times 11 = 44 \]
\[ 10^2 = 100 \]
- Now, substitute these values back into the equation:
\[ OA^2 = 44 + 100 = 144 \]

5. **Find the Radius:**
- To find OA (the radius), take the square root of both sides:
\[ OA = \sqrt{144} = 12 \text{ cm} \]

### Conclusion:
The radius of the circle is \(12\) cm.