In the given figure, a circle is inscribed in Δ PQR, 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.

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 02 Dec 2022 Shift 1)

Answer 1

Given:

In Δ PQR,

PQ = 15 cm, QR = 11 cm and RP = 13 cm.

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

Concept Used:

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

Calculation:

A circle is inscribed in Δ 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

∴ Option 4 is the correct answer.

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