Question

a circle is inscribed in a ∆ABC,sach that it touch the sides AB,BC and CA at point D,E and F respectively. if the length of sides AB,AC and CA are 12cm,8cm and 10cm respectively, find the length of AD,BE and CF.

Answer 1

Let x be AD
y be BE and
z be CF

AD = AF = x ( tangents to a girl Le front he same point are equal)
BD = BE = y (“)
CE = CF = z (“)

AB = x + y = 12
x = 12-y ————— 1
AC = x +z = 10
x = 10 - z ———————- 2
From 1 and 2,
12 - y = 10-z
y-z =12-10 = 2
y = 2+z
BC = y+z = 8
2 +z +z =8
2z = 6
z = 3
y = 2 +z = 2 + 3 = 5
x = 12 - y = 12- 5 = 7

AD = 7
BE = 5
CF = 3