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 = 18 cm. QR = 13 cm and RP = 15 cm, then find the length of PD. 

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  1. 10 cm
  2. 8 cm
  3. 15 cm
  4. 12 cm

Answer (Detailed Solution Below)

Option 1 : 10 cm
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Detailed Solution

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Given:

 PQ = 18 cm, QR = 13 cm and RP = 15 cm

Concept used:

A pair of tangent lines drawn from an external point to a circle are equal in length.

So, PF = PD, DQ = EQ and FR = RE

Calculation

Let PD be x cm,

then QD = (18 – x) cm

⇒ QE = (18 – x) cm

⇒ RE = 13 – (18 – x) = x – 5

⇒ RF = (x – 5)

⇒ PF = 15 – (x - 5) = 20 – x

⇒ 20 – x = x

⇒ 2x = 20

⇒ x = 20/2

⇒ x = 10 cm

⇒ PD = 10

The answer is 10.

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