Question

A circle is inscribed in a triangle $ABC,$ having sides $8cm,$ $10cm$ and $12cm.$ Find $AD,BE$ and $CF$ $($ these 3 are altitudes of triangle $ABC$) $.$

Answer 1

Given$,$

$x+y=8cm$ ....$\left(1\right)$

$y+z=12cm$ .....$\left(2\right)$

$x+z=10cm$ .....$\left(3\right)$

Adding $\left(1\right),$ $\left(2\right)$ and $\left(3\right),$ we get

$2(x+y+z)=30$

$x+y+z=30/2$

$x+y+z=15$ .....$\left(4\right)$

Equation $\left(4\right)-\left(2\right),$ we get

$x+12=15$

$x=15-12$

$x=3$

Equation $\left(4\right)-\left(3\right),$ we get

$10+y=15$

$y=15-10$

$y=5$

$\left(4\right)-\left(1\right),$ we get

$8+z=15$

$z=15-8$

$z=7$

So$,$

$AD=3cm$

$BE=5cm$

$CF=7cm$ Answer.