In the given figure, a circle inscribed in ΔPQR 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?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e PS = 8.5 cm, QT = 6.5 cm and RU = 3.5 cm
Let PS = xcm
⇒ SQ = 15 - x
The tangent from an external point to the circle are equal in length
⇒ QT = SQ = 15 - x
QR = 10 cm
⇒ TR = UR = 10 - (15 - x) = x - 5
And
RP = 12 cm
⇒ PU = 12 - (x - 5) = 17 - x
PU = PS
⇒ 17 - x = x
⇒ x = 8.5 cm
PS = 8.5 cm
⇒ QT = 15 - x = 6.5 cm
⇒ RU = x - 5 = 8.5 - 5 = 3.5 cm