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 PB + AR is equal to:

Solution (By Examveda Team)

2(x + y + z) = 32
x + y + z = 16
AB - AC = x - y
x - y = 2 . . . . . . . (i)
AB - BC = z - y
z - y = 4 . . . . . . . (ii)
Add equation (i) + equation (ii)
x + z - 2y = 6
$$\frac{{{\text{x}} + {\text{z}} - 6}}{2}$$   = y
x + y + z = 16
x + z + $$\frac{{{\text{x}} + {\text{z}} - 6}}{2}$$   = 16
2(x + z) + x + z - 6 = 32
3(x + z) = 38
x + z = $$\frac{{38}}{3}$$
PB + AR = $$\frac{{38}}{3}$$