In the given figure, a circle inscribed in $$\triangle$$ PQR touches its sides PQ, QR and RP at points S, T and U,respectively. If PQ = 15 cm, QR= 10 cm, and RP = 12 cm, then find the lengths of PS, QT and RU?

Given, PQ = 15 cm, QR= 10 cm, and RP = 12 cm

PS and PU are tangents to the circle from point P.

$$\Rightarrow$$  PS = PU

Let PS = PU = x

QT and QS are tangents to the circle from point Q.

$$\Rightarrow$$  QT = QS

Let QT = QS = y

RU and RT are tangents to the circle from point R.

$$\Rightarrow$$  RU = RT

Let RU = RT = z

PQ = 15 cm

$$\Rightarrow$$ PS + QS = 15

$$\Rightarrow$$ x + y = 15 ........(1)

Similarly,

y + z = 10 ..........(2)

z + x = 12 ..........(3)

Adding (1), (2), (3)

x + y + z = 18.5 .......(4)

From (1) and (4), z = 3.5 cm

From (2) and (4), x = 8.5 cm

From (3) and (4), y = 6.5 cm

$$\therefore\ $$PS = 8.5 cm, QT = 6.5 cm and RU = 3.5 cm

Hence, the correct answer is Option B