In the given figure, a circle inscribed in △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?

PS = 8.5 cm, QT = 6.5 cm and RU = 3.5 cm

From a common point if two tangents are drawn that touches circle , then length of both the tangents are same.

⇒ PS = PU , SQ = QT , RT = RU

PQ = 15 cm

Let us consider that PS = a cm

⇒ SQ = 15 - a

We know ,  PS = PU

⇒ PU =  a

& QT = 15 - a cm

RQ = 10 cm ( Given ) 

RT = 10 - 15 + a = a - 5

RT = RU

⇒ RU = a - 5

PU = 12 - a + 5 = 17 - a

We know that ,

17 - a = a

2a = 17

a = 8.5 cm

Now, PS = 8.5 cm

QT = 15 - a = 15 - 8.5 = 6.5 cm

RU = 8.5 - 5 = 3.5 cm

Answer :- PS = 8.5 cm, QT = 6.5 cm and RU = 3.5 cm