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Question

# A Circle is inscribed in triangle ABC having sides 8 cm, 10 cm, and 12 cm as shown in the given figure. Find AD?

A
2.5 cm
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B
4 cm
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C
3 cm
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D
5 cm
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Solution

## The correct option is D 5 cm AB= 8 cm, AC = 12 cm and BC = 10 cm Let AD = x then BD = (8-x) And also, AD = AF = x [ Tangents drawn from the same external points are equal to each other.] Then, CF = (12-x) Similarly, BD = BE = (8-x) and CE = CF =(12 -x) As we know, BC = BE +CE 10 = (8-x) +(12-x) 10 = 20-2x 2x=10 x=5 AD = x = 5 Hence, c is the correct option.

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