Question

ABC is a right angled triangle in which $\angle A={90}^{\circ }$. Find the area of the non-shaded region if AB = 6 cm, BC=10 cm & O is the center of the incircle of ABC.

• A.
  
• B.
  
• C.
  
• D.
  

Answer 1

The correct option is D

BC =10cm; AB =6cm; AC =8cm (Pythagoras Property)
Area of the =$\frac{1}{2}\times 6\times 8=24c{m}^2$
Let the radius of the in circle be r.
Area of $(\Delta AOC+\Delta BOC+\Delta AOB)$ Area of $\Delta ABC$
$\Rightarrow (\frac{1}{2}\times 10\times r+\frac{1}{2}\times 8\times r+\frac{1}{2}\times 6\times r)=24\Rightarrow \frac{1}{2}\times r\times [10+8+6]=24\Rightarrow r=2cm$
Area of circle =$\frac{22}{7}\times 2\times 2=\frac{88}{7}c{m}^2$
Area of shaded region =$24-\frac{88}{7}=\left(\frac{168-88}{7}\right)=\frac{80}{7}c{m}^2$