In figure, a circle inscribed in 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.

Open in App

Solution

We know that AD= AF
BD=BE
CE=CF

Let AD= AF= $x$
BD=BE= $y$

CE=CF= $z$

Then $x + y = 12$
$y + z = 8$

$x + z = 10$

On Solving above equation we get $x = 7, y = 5, z = 3$

So AD=7 , BE=5 , CF= 3

Suggest Corrections

Similar questions

Q. In fig., a circle is inscribed in triangle

A B C

touches its sides

A B, B C

and

A C

at points

D, E

and

F

respectively. If

A B = 12

cm,

B C = 8

cm and

A C = 10

cm, then find the length of

A D, B E

and

C F

In the given figure, a circle inscribed in a triangle ABC, touches the sides AB, BC and AC at points D, E and F respectively. If AB = 12 cm, Bc = 8 cm and AC = 10 cm, find the lengths fo AD, BE and CF.

In Fig., a circle inscribed in 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.