Question

The incircle of a triangle ABC, touches its sides AB,BC and AC at points D, E and F respectively. If AB =12 cm, BC= 8 cm and AC = 10 cm, then find the lengths of AD, BE and CF.

Answer 1

line from centre ie radius of a cirle bisects the tangent

Answer 2

The tangents drawn from an external point to a circle are equal.

$\therefore$ $\sf{AD=AF=x(say)}$

$\sf{BD=BE=y(say)}$

$\sf{CE=CF=z(say)}$

Now,

$\sf{AB=x+y=12cm}$

$\sf{BC=y+z=8cm}$

$\sf{AC=z+x=10cm}$

On adding,

= $\sf{2(x+y+z)=30}$

= $\sf{x+y+z=15cm}$

Hence,

$\sf{AD=15-8=7cm}$ ,

$\sf{BE=15-10=5cm}$ ,

$\sf{CF=15-12=3cm}$