Question

$ABC$ is a triangle in which $\angle B={90}^o,BC=48cm$ and $AB=14cm$. A circle is inscribed in the triangle, whose centre is $O$. Find radius $r$ of in-circle.

• A. $4cm$
• B. $6cm$
• C. $7cm$
• D. $9cm$

Answer 1

The correct option is B $6cm$

R.E.F image

$A{C}^2=A{B}^2+B{C}^2$

$=\sqrt{(14{)}^2+(48{)}^2}=50cm$

$Ar.of\Delta ABC=Ar.of\Delta AOB+Ar.of\Delta BOC+Ar.of\Delta AOC$

$\frac{1}{2}\times b\times h=\frac{1}{2}\times b_1\times h_1+\frac{1}{2}\times b_2\times h_2+\frac{1}{2}\times b_3\times h_3$

$\frac{1}{2}\times 14\times 48=\frac{1}{2}\times 14\times r+\frac{1}{2}\times 48\times r+\frac{1}{2}\times 50\times r$

$336=7r+24r+25r$

$336=56r$

$r=6$