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?
Answer & explanation
Correct answer: option 2
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