Question

Example 4. The sides of AABC, AB, BC and
CA touches a circle of 4 cm radius at points L, M
and N respectively. If AN = 6 cm, CN = 8 cm,
then find the perimeter of ABC.
Solution : Let in the circle, the center of AABC
is 'O'.
6 cm
6 cm
L
N
b
x cm
y
8 cm
14 cm
B
3tr
x cm
С
8 cm
a​

Answer 1

Step-by-step explanation:

In △ABC

AB, BC and AC touches the circle at the point P, Q and R respectively.

∴ BC+AP=AC+PB

⟹ 13+7=AC+PB

⟹ AC=20−PB

Perimeter of △ABC=AB+BC+AC

=AP+PB+13+20−PB

=7+13+20=40

∴ Perimeter of △ABC is 40 cm.

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