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?

32

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