question_answer

\[\Delta \,ABC\] is a right angled triangle \[AB=6\text{ }cm,\]\[BC=8\text{ }cm\] and \[AC=10\text{ }cm\] then the radius of the in circle is -

A)  1 cm                           

B)  2 cm

C)  3 cm                           

D)  4 cm

Correct Answer: B

Solution :

Area of \[\Delta \text{ }ABC=\frac{1}{2}\times 6\times 8=24\text{ }c{{m}^{2}}\] Area of \[\Delta \text{ OA}C=\frac{1}{2}\times a\times 10=5a\,c{{m}^{2}}\] Similarly area of \[\Delta \,OBC\] and \[\Delta \,OAB\] will be \[4\text{ }a\text{ }c{{m}^{2}}\]and \[\text{3 }a\text{ }c{{m}^{2}}\] respectively. Area of \[\Delta \text{ }ABC\] = Area of             \[(\Delta \text{ OAC+}\Delta \,\text{OBC+}\Delta \,OAC)\] \[24=5a+4a+3a=12a=24=a=2\,cm\] Radius of in circle = 2 cm