A circle is inscribed in a triangle ABC, having sides 8 cm , 10 cm and 12 cm. Find AD , BE and CF ( these 3 are altitudes of triangle ABC).

Here

 x+y=8 ...(1)

y+z=12...(2)

x+z=10...(3)

Adding (1),(2) and (3),

2(x+y+z)=30

x+y+z=15 ..(4)

(4)-(2) ==>x=3

(4)-(3)==>y=5

(4)-(1)==>x=7

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