Quadrilateral ABCD circumscribes a circle. If AB = 8 cm, BC = 7 cm and CD = 6 cm, then the length of AD is:

Options

A. 7 cm
B. 6.8 cm
C. 7.5 cm
D. 6 cm

Answer

To find the length of side AD in the quadrilateral ABCD that circumscribes a circle, we can use the property of tangential quadrilaterals. The property states that the sum of the lengths of opposite sides of a tangential quadrilateral is equal.

### Step-by-step Solution:

1. **Identify the sides of the quadrilateral**:
- Let AB = 8 cm
- Let BC = 7 cm
- Let CD = 6 cm
- Let AD = x (this is what we need to find)

2. **Use the property of tangential quadrilaterals**:
According to the property, the sum of the lengths of opposite sides is equal:
\[ AB + CD = BC + AD \]

3. **Substitute the known values into the equation**:
\[ 8 + 6 = 7 + x \]

4. **Simplify the equation**:
\[ 14 = 7 + x \]

5. **Solve for x**:
\[ x = 14 - 7 \]
\[ x = 7 \]

6. **Conclusion**:
The length of side AD is 7 cm.

### Final Answer:
AD = 7 cm