Question

In Figure 5, a circle is inscribed in a triangle PQR with PQ = 10 cm, QR = 8 cm and PR =12 cm. Find the lengths of QM, RN and PL ?

Answer 1

Given: In ΔPQR, PQ = 10, QR = 8 cm and PR = 12 cm.

We know that, the lengths of tangents drawn from an external point to a circle are equal.

∴ QM = OL = x (Say)

RM = RN = y (Say)

PL = PN = z (Say)

QR = QM + MR = x + y = 8 cm ……(1)

PQ = PL + LQ = z + x = 10 cm ……(2)

PR = PN + NR = z + y = 12 cm ……(3)

Adding (1), (2) and (3) , we have

(x + y) + (z + x) + (z + y) = (8 + 10 + 12) = 30 cm

∴ 2(x + y + z) = 30 cm

⇒ x + y + z = 15 cm …..(4)

From (2) and (4), we have

10 + y = 15

∴ y = 5

From (3) and 4, we have

12 + x = 15

∴ x = 3

From (1) and (4), we have

⇒ z + 8 = 15

⇒ z = 7

∴ QM = x = 3 cm

RN = y = 5 cm

PL = z = 7 cm