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In the given figure, a circle is inscribed in such that it touches the sides PQ, QR and RP at points D, E, F, respectively. If the lengths of the si
Question

In the given figure, a circle is inscribed in 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.

A.

9 cm

B.

8 cm

C.

7.5 cm

D.

8.5 cm

Correct option is D

Given:
PQ = 15 cm
QR = 11 cm
RP = 13 cm
Concept Used:  
If two tangents are drawn to a circle from a external point , then the length of the two tangents are equal 
Solution:
According to the question 

17x=x 2x=17 x=172 x=8.5 cm17-x = x\\ \ \\2x = 17 \\ \ \\ x= \frac{17}{2}\\ \ \\ x=8.5\:cm​​

Thus, option (d) is correct.

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