Question

In the given figure, AB=14 cm, radius of in circle of $\Delta ABC$ is 4 cm, AF = 6 cm, AE = 6 cm and BD=8 cm. Find AC and BC.

• A. 14 cm , 16 cm
• B. 11 cm , 13 cm
• C. 12 cm , 14 cm
• D. 13 cm , 15 cm

Answer 1

The correct option is C 12 cm , 14 cm

R.E.F image

$△AIE$ $△EIC$

$A{I}^2=A{E}^2+I{E}^2$ $AI=IC$

$A{I}^2=6^2+4^2$ $\therefore I{C}^2=E{I}^2+C{E}^2$

$A{I}^2=52$ $6^2+4^2=4^2+C{E}^2$

$CE=6cm=x$

$△ICG$ $AC=6+x=12cm$

$I{C}^2=C{G}^2+G{I}^2$ $BC=8+x=14cm$

$6^2+4^2=x^2+4^2$

$x=6cm$