The diameter of a circle is 20 cm. There are two parallel chords of length 16 cm . And 12 cm. Find the distance between these chords if chords are on the:
(i) same side
(ii) opposite side of the centre.

Explanation

To solve the problem step by step, we will find the distance between the two parallel chords of lengths 16 cm and 12 cm in a circle with a diameter of 20 cm. We will consider both cases: when the chords are on the same side of the center and when they are on opposite sides.

### Given:
- Diameter of the circle = 20 cm
- Radius of the circle (r) = Diameter / 2 = 20 / 2 = 10 cm
- Length of chord AB = 12 cm
- Length of chord CD = 16 cm

### Step 1: Find the lengths of the segments from the center to the chords.
1. **For chord AB (length = 12 cm):**
- Half of chord AB = AB/2 = 12/2 = 6 cm
- Let the distance from the center O to chord AB be ON.
- Using the Pythagorean theorem in triangle OMB (where M is the midpoint of AB):
\[ OB^2 = OM^2 + MB^2 \]
\[ 10^2 = ON^2 + 6^2 \]
\[ 100 = ON^2 + 36 \]
\[ ON^2 = 100 - 36 = 64 \]
\[ ON = \sqrt{64} = 8 \text{ cm} \]

2. **For chord CD (length = 16 cm):**
- Half of chord CD = CD/2 = 16/2 = 8 cm
- Let the distance from the center O to chord CD be OM.
- Using the Pythagorean theorem in triangle OCN (where N is the midpoint of CD):
\[ OC^2 = ON^2 + NC^2 \]
\[ 10^2 = OM^2 + 8^2 \]
\[ 100 = OM^2 + 64 \]
\[ OM^2 = 100 - 64 = 36 \]
\[ OM = \sqrt{36} = 6 \text{ cm} \]

### Step 2: Calculate the distance between the chords.
1. **(i) If both chords are on the same side of the center:**
- The distance between the two chords (MN) = OM + ON
\[ MN = 8 + 6 = 14 \text{ cm} \]

2. **(ii) If the chords are on opposite sides of the center:**
- The distance between the two chords (MN) = OM + ON
\[ MN = 8 + 6 = 14 \text{ cm} \]

### Final Answers:
- (i) Distance between the chords on the same side = 14 cm
- (ii) Distance between the chords on opposite sides = 14 cm