A circle is inscribed in the triangle PQR whose sides are given as PQ = 12 cm, PR = 10 cm and QR = 14 cm as shown in the figure. The value of QY × PZ is?
Answer & explanation
Correct answer: option 4
Let QY = a
QY = QX = a .....................(i) (Tangent from same points)
similarly,
PX = PZ = b, ....................(ii)
RZ = RY = c .....................(iii)
adding (i), (ii) and (iii), we get
⇒ 2(a + b + c) = 14 + 12 + 10 = 36
⇒ a + b + c = 18 ...........(iv)
Here,
a + c = QR = 14
⇒ b = 4 = PZ from (iv)
b + c = PR = 10
⇒ a = 8 = QY from (iv)
Therefore,
QY × PZ = 8 × 4 = 32