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

2.5 cm

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4 cm

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3 cm

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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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In fig., a circle is inscribed in a triangle ABC having side BC = 8 cm, AC = 10 cm and AB = 12 cm. Find AD, BE and CF. [3 MARKS]

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