Question

A circle is inscribed in a triangle ABC having sides 8cm, 10cmand 12cn.find AD,BEand cf

Answer 1

AD=AF=x,BD=BE=y, &CE=CF=z
form the equation of the three;AB=AD+DB=x+y=8...................(i)
                                                BC=BE+EC=y+z=10..................(ii)
                                                AC=AF+FC=x+y=12..................(iii)
Add the three equations;
AB=AD+DB=x+y=8)+BC=BE+EC=y+z=10)+AC=AF+FC=x+y=12)=2(x+y+z)=30
therefore;x+y+z=15..............(iv)
solve the three equations following the trend below;
(i)&(ii)=z=7
(ii)&(iv)=x=5
(iii)&(iv)=y=3
hence,AD=x=5cm
           BE=y=3cm
           CF=z=7cm

Answer 2

Step-by-step explanation:

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.