A circle is inscribed in ΔABC, touching AB, BC and AC at the points P, Q and R respectively. If AB - BC = 4 cm, AB - AC = 2 cm, and the perimeter of ΔABC= 32 cm, then AC (in cm) = ?

$\frac{32}{3}$

AB - BC = 4    ..(1)

AB - AC = 2    ..(2)

Perimeter of ABC = 32  

AB + BC + CA = 32    ..(3)

Adding equations (1), (2) and (3)

32 = 3AB - 6

3AB = 32 + 6

3AB = 38

AB = \(\frac{38}{3}\)

Now,

⇒ AC = AB - 2

⇒ AC = [\(\frac{38}{3}\) - 2]

⇒ AC = \(\frac{32}{3}\) cm

Therefore, AC is \(\frac{32}{3}\) cm.