Question

In the given figure, a circle touches all the four sides of a quadrilateral ABCD whose sides AB = 6cm, BC =7cm and CD =4cm.Then AD=

• A. 2 cm
• B. 3 cm
• C. 5 cm
• D. 6 cm

Answer 1

Answer: (B)

3 cm

Each vertex must be the same distance from both the points where it touches the circle.
Let a represent that distance from A,
b represent that distance from B,
and similarly for c and d.

Then

$a+b=6=AB$ -- (1)

$b+c=7=BC$ --- (2)
$c+d=4=CD$ -- (3)
Subtracting $3$ from $2$, we get
$b-d=3$ -- (4)

Subtracting $4$ from $1$, we get
$a+d=3$ --- (5)

Since $a+d=$ the length of AD, that length is$3cm.$