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 6 cm and 8 cm, then radius of the circle is :

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

Answer 1

Answer: (B)

2 cm

Given a right triangle BAC with measures of BA = 6cm, AC = 8cm and BC = 10cm.
The radius of the incentre is given by $\frac{areaof\Delta BAC}{semiperimeterof\Delta BAC}=\frac{\frac{1}{2}\ast 6\ast 8}{\frac{1}{2}(6+8+10)}=\frac{24}{12}=2$.
The radius of the incircle is 2cm.