Quadrilateral `ABCD` is circumscribed to a circle. If `AB=6cm`, `BC=7cm` and `CD=4cm` then the length of `AD` is

Options

A. `3cm`
B. `4cm`
C. `6cm`
D. `7cm`

Explanation

To find the length of \( AD \) in the circumscribed quadrilateral \( ABCD \), we can use the property of a tangential quadrilateral, which states that the sum of the lengths of the opposite sides is equal. Specifically, we have:

\[ AB + CD = AD + BC \]

### Step-by-step Solution:

1. **Identify the given lengths**:
- \( AB = 6 \, \text{cm} \)
- \( BC = 7 \, \text{cm} \)
- \( CD = 4 \, \text{cm} \)
- We need to find \( AD \).

2. **Set up the equation using the property of tangential quadrilaterals**:
\[ AB + CD = AD + BC \]

3. **Substitute the known values into the equation**:
\[ 6 + 4 = AD + 7 \]

4. **Simplify the left side**:
\[ 10 = AD + 7 \]

5. **Isolate \( AD \)**:
\[ AD = 10 - 7 \]

6. **Calculate the value of \( AD \)**:
\[ AD = 3 \, \text{cm} \]

### Final Answer:
The length of \( AD \) is \( 3 \, \text{cm} \).