In a circle of radius 5 cm, PQ and RS are two parallel chords of lengths 8 cm and 6 cm respectively. Calculate the distance between the chords if they are on:
the same side of the centre.

Answer

To solve the problem, we will follow these steps:

1. **Understand the Geometry**: We have a circle with a radius of 5 cm, and two parallel chords PQ and RS with lengths of 8 cm and 6 cm respectively. Both chords are on the same side of the center of the circle.

2. **Identify the Midpoints of the Chords**:
- The midpoint of chord PQ divides it into two equal segments of 4 cm each (since the total length is 8 cm).
- The midpoint of chord RS divides it into two equal segments of 3 cm each (since the total length is 6 cm).

3. **Draw Perpendiculars from the Center**:
- Draw a perpendicular from the center O of the circle to each chord. Let A be the foot of the perpendicular from O to PQ, and B be the foot of the perpendicular from O to RS.

4. **Apply the Pythagorean Theorem**:
- For triangle OAQ (where AQ = 4 cm):
\[ OQ^2 = OA^2 + AQ^2 \]
\[ 5^2 = OA^2 + 4^2 \]
\[ 25 = OA^2 + 16 \]
\[ OA^2 = 25 - 16 = 9 \implies OA = 3 \text{ cm} \]

- For triangle OBS (where BS = 3 cm):
\[ OS^2 = OB^2 + BS^2 \]
\[ 5^2 = OB^2 + 3^2 \]
\[ 25 = OB^2 + 9 \]
\[ OB^2 = 25 - 9 = 16 \implies OB = 4 \text{ cm} \]

5. **Calculate the Distance Between the Chords**:
- The distance between the two chords (AB) is given by:
\[ AB = OB - OA \]
\[ AB = 4 \text{ cm} - 3 \text{ cm} = 1 \text{ cm} \]

Thus, the distance between the chords PQ and RS is **1 cm**.