If a circle with radius of 10 cm and two parallel chords 16 cm and 12 cm and they are on the same side of the centre of the circle, then the distance between the two parallel chords is.

Options

A. 5 cm
B. 8 cm
C. 2 cm
D. 3 cm

Answer

To find the distance between the two parallel chords in a circle with a radius of 10 cm, where the lengths of the chords are 16 cm and 12 cm, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Circle and Chords**:
- We have a circle with a radius \( r = 10 \) cm.
- The lengths of the two chords are \( AB = 16 \) cm and \( CD = 12 \) cm.

2. **Determine the Lengths of Half the Chords**:
- For chord \( AB \):
\[ AK = KB = \frac{AB}{2} = \frac{16}{2} = 8 \text{ cm} \]
- For chord \( CD \):
\[ CQ = QD = \frac{CD}{2} = \frac{12}{2} = 6 \text{ cm} \]

3. **Use Pythagoras Theorem for Triangle \( AOK \)**:
- In triangle \( AOK \):
\[ OA^2 = OK^2 + AK^2 \]
- Substituting the known values:
\[ 10^2 = OK^2 + 8^2 \]
\[ 100 = OK^2 + 64 \]
\[ OK^2 = 100 - 64 = 36 \]
\[ OK = \sqrt{36} = 6 \text{ cm} \]

4. **Use Pythagoras Theorem for Triangle \( OQC \)**:
- In triangle \( OQC \):
\[ OC^2 = OQ^2 + CQ^2 \]
- Substituting the known values:
\[ 10^2 = OQ^2 + 6^2 \]
\[ 100 = OQ^2 + 36 \]
\[ OQ^2 = 100 - 36 = 64 \]
\[ OQ = \sqrt{64} = 8 \text{ cm} \]

5. **Calculate the Distance Between the Chords**:
- The distance \( KQ \) between the two chords is given by:
\[ KQ = OQ - OK \]
- Substituting the values:
\[ KQ = 8 - 6 = 2 \text{ cm} \]

### Final Answer:
The distance between the two parallel chords is **2 cm**.

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