Question

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).

Answer 1

Here given,
x+y =  8 cm   ....(1) 
y+z = 12 cm .....(2)
x+z = 10 cm .....(3)
Adding (1), (2) and (3), we get 
2(x+y+z) = 30
x+y+z = 30/2
x+y+z = 15  .....(4)
(4) - (2), we get
x+12 = 15
x = 15 - 12
x =3
(4) - (3),  we get
10+y = 15
y = 15 - 10
y = 5
(4) - (1), we get 
8+z = 15
z = 15 - 8
z = 7
So,
AD = 3 cm
BE = 5 cm
CF = 7 cm  Answer.

Answer 2

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