Question
Download Solution PDFIn 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.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
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.
Last updated on Jun 13, 2025
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