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.
Answer & explanation
Correct answer: option 4
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.