Question

In below figure $\Delta ABC$ is a right angle triangle in which $\angle B={90}^o$ and $BC=6$ cm and $AB=8$ cm .Then radius of incircle will be:

• A. $5cm$
• B. $4cm$
• C. $3cm$
• D. $2cm$

Answer 1

The correct option is D $2cm$

$AB,BC$ and $CA$ are tangents to the circle $P,N$ and $M$

$\therefore OP=ON=OM=r\left(radius\right)$

Area of $△ABC=\frac{1}{2}\times 6\times 8=24{cm}^2$

By Pythagoras,

${AC}^2={AB}^2+{BC}^2$

${CA}^2=8^2+6^2$

$CA=10cm$

Area of $△=$ Area of $△OAB+$ Area of $△OBC+$ Area of $△OCA$

$24=\frac{1}{2}r\times AB+\frac{1}{2}r\times BC+\frac{1}{2}r\times CA$

$24=\frac{1}{2}r(AB+BC+CA)$

$r=\frac{2\times 24}{AB+BC+CA}$

$r=\frac{48}{6+8+10}$

$r=2$