The difference in lengths of parallel sides of a trapezium inscribed in a circle is 6 cm, if distance between parallel sides is 4 cm then difference in lengths of its non parallel side is

Options

A. A)10 cm
B. B)5 cm
C. C)0 cm
D. D)Cannot be determined

Answer

To solve the problem, we need to analyze the properties of a trapezium inscribed in a circle.

### Step-by-Step Solution:

1. **Understand the Properties of the Trapezium**:
- A trapezium (or trapezoid) inscribed in a circle is known as a cyclic trapezium. In a cyclic trapezium, the non-parallel sides are equal in length.

2. **Define the Parallel Sides**:
- Let the lengths of the parallel sides be \( x \) and \( x + 6 \) cm, where \( x + 6 \) is the longer side and \( x \) is the shorter side.

3. **Distance Between Parallel Sides**:
- The distance between the parallel sides is given as 4 cm.

4. **Properties of Non-Parallel Sides**:
- Since the trapezium is cyclic, the non-parallel sides (let's denote them as \( AD \) and \( BC \)) are equal in length. Let the length of each non-parallel side be \( k \).

5. **Difference in Lengths of Non-Parallel Sides**:
- Since both non-parallel sides are equal, the difference in lengths of the non-parallel sides can be calculated as:
\[ AD - BC = k - k = 0 \]

6. **Conclusion**:
- Therefore, the difference in lengths of the non-parallel sides of the trapezium is \( 0 \) cm.

### Final Answer:
The difference in lengths of the non-parallel sides is **0 cm**.

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