In the given figure, a circle is inscribed in ΔPQR, such that it touches the sides PQ, QR and RP at points D, E, F, respectively. If the lengths of the sides PQ = 15 cm, QR = 11 cm and RP = 13 cm, then find the length of PD.

8.5 cm

Concept

Tangents drawn from a point to the circle are equal in length.

Calculation

A circle is inscribed in \(\Delta \)PQR, such that it touches the sides PQ, QR and RP at points D, E, F respectively.

⇒ PD = PF = x

⇒ QD = QE = y

⇒ RE = RF = z

All are tangents,

⇒ PD + PF + QD + QE + RE + RF = PQ + QR + RP

⇒ x + x + y + y + z + z = 39

⇒ 2x + 2(y + z) =  39

Here,

y + z = QE + ER = RQ

and we have RQ = 11

⇒ 2x + 2(11) = 39

⇒ 2x + 22 = 39

⇒ 2x = 17

⇒ x = 8.5

⇒ PD = 8.5 cm

Therefore, PD is 8.5 cm.