Question

$ABC$ is a right-angle triangle, right angled at $A$. A circle is inscribed in it. The lengths of the two sides containing the right angle are $6cm$and$8cm$, then radius of the circle is

• A. $3cm$
• B. $2cm$
• C. $4cm$
• D. $8cm$

Answer 1

Answer: (B)

$2cm$

$△ABCisrightanglewhere\angle A=90andAB=6cmandAC=8cmObethecenterofcircleandristheradiusofcircleAB,BCandCAaretangentstocircleatP,NandM.Areaof△ABC=\frac{1}{2}\times AB\times h=\frac{1}{2}\times 6\times 8=24{cm}^{2}Bypythagoreastheorm{BC}^2={AC}^2+{AB}^2=8^2+6^2=64+36=100BC=\sqrt{100}=10Area△ABC=Ar△OAB+Ar△OBC+Ar△OCA24=\frac{1}{2}\times r\times AB+\frac{1}{2}\times r\times BC+\frac{1}{2}\times r\times CA24=\frac{1}{2}r(AB+BC+CA)48=r(6+8+10)\Rightarrow r=\frac{48}{24}=2cmHenceoption\left(B\right)istherightanswer$