Question

A circle is inscribed in a triangle ABC having sides 16cm,20cm and 24cm. Find AD,BE and CF.

Answer 1

The value of $AD=10\ cm,BE=6\ cm\ and\ CF=14\ cm$

Step-by-step explanation:

Given,

A circle is inscribed in a $\triangle ABC$ having sides $16\ cm,20\ cm\ and\ 24\ cm$

From figure,

$AD=x\ cm,BE=y\ cm\ and\ CF=z\ cm$

$x+y=16$__1

$y+z=20$__2

$x+z=24$__3

From equation-2,

$y=20-z$__4

Plug the value in equation-1,

$x+20-z=16$

⇒$x-z=-4$__5

Add equation-1 and 5,

$2x=20$

⇒$x=10$

From equation-3,

$10+z=24$

⇒$z=14$

And from equation-4,

$y=20-14$

⇒$y=6$

So, The value of $AD=10\ cm,BE=6\ cm\ and\ CF=14\ cm$

Answer 2

Step-by-step explanation:

hence AD=14, AF=14,

DB=10, BE=10

CE=6, CF=6