In the given figure, a circle is inscribed in △PQR, such that it touches the sides PQ, QR, and RP at points D, E, and F respectively. If the lengths of the sides PQ = 15 cm, QR = 11 cm, and RP = 13 cm, then find the length of PD.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 8.5 cm.
The lengths of tangents drawn from an external point to a circle are equal
Let the value of ER = x
Hence using the concept given;
⇒ ER = FR = x
⇒ PF = 13 - x and PD = 13 - x (PF = PD)
⇒ QE = 11 - x and QD = 11 - x (QE = QD)
Now, QP = PD + QD
⇒ 15 = 13 - x + 11 - x
⇒ 2x = 24 - 15
⇒ x = 4.5
We know that, PD = 13 - x = 13 - 4.5 = 8.5 cm