Two parallel chords of lengths 30cm and 16cm are drawn on the opposite sides of the centre of a circle of radius 17cm. Find the distance between the chords.

Answer

To solve the problem of finding the distance between two parallel chords of lengths 30 cm and 16 cm in a circle of radius 17 cm, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information**:
- Length of the first chord (AB) = 30 cm
- Length of the second chord (CD) = 16 cm
- Radius of the circle (r) = 17 cm

2. **Determine the Half-Lengths of the Chords**:
- The first chord (AB) is bisected, so half of its length is:
\[ \frac{30}{2} = 15 \text{ cm} \]
- The second chord (CD) is also bisected, so half of its length is:
\[ \frac{16}{2} = 8 \text{ cm} \]

3. **Set Up Right Triangles**:
- From the center of the circle (O), draw perpendiculars to the chords. Let the distance from the center to the first chord (AB) be \( x \) and to the second chord (CD) be \( y \).
- For chord AB, we have a right triangle OAB:
\[ OA^2 + OB^2 = r^2 \implies x^2 + 15^2 = 17^2 \]
- For chord CD, we have a right triangle OCD:
\[ OC^2 + OD^2 = r^2 \implies y^2 + 8^2 = 17^2 \]

4. **Calculate \( x \)**:
- Substitute the values into the equation for chord AB:
\[ x^2 + 15^2 = 17^2 \]
\[ x^2 + 225 = 289 \]
\[ x^2 = 289 - 225 = 64 \]
\[ x = \sqrt{64} = 8 \text{ cm} \]

5. **Calculate \( y \)**:
- Substitute the values into the equation for chord CD:
\[ y^2 + 8^2 = 17^2 \]
\[ y^2 + 64 = 289 \]
\[ y^2 = 289 - 64 = 225 \]
\[ y = \sqrt{225} = 15 \text{ cm} \]

6. **Find the Distance Between the Chords**:
- The distance between the two chords is the sum of \( x \) and \( y \):
\[ \text{Distance} = x + y = 8 + 15 = 23 \text{ cm} \]

### Final Answer:
The distance between the two chords is **23 cm**.