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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 Circle is inscribed in triangle ABC having sides 8 cm, 10 cm, and 12 cm as shown in the given figure. Find AD?
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Solution
The correct option is C 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.
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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