Question : In the given figure, a circle is inscribed in $\triangle$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 = 18 cm, QR = 13 cm, and RP = 15 cm, find the length of PD.
Option 1: 10 cm
Option 2: 8 cm
Option 3: 15 cm
Option 4: 12 cm
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Correct Answer: 10 cm
Solution :
Given: PQ = 18 cm, QR = 13 cm, and RP = 15 cm
We know that two tangents to a circle from the same external point are equal.
So, PF = PD
Let the length of PD be $x$.
DQ = $18-x$ = EQ
FR = $15-x$ = RE
Now, QR = RE + EQ
⇒ $13=15-x+18-x$
⇒ $2x=33-13$
$\therefore x =10$
Hence, the correct answer is 10 cm.
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