Question

ABC is a triangle with $\angle A={30}^0$, BC = 10cm. The area of the circumcircle of the triangle is

• A. 100π sq cm
• B. 5 sq cm
• C. 25 sq cm
• D. sq cm

Answer 1

The correct option is A

100π sq cm

$In\Delta ABC,\angle A={30}^{0}BC=10cm\text{Let O is the centre of circle}\therefore \angle BOC={60}^0\text{and OB and OC are the radius}\therefore \angle OBC=\angle OCB={60}^0\Rightarrow \Delta OBC\text{is an equilateral triangle}.\therefore \text{Radius of circle is OB=OC=BC=10 cm}\text{Now, area of the circumcircle is}\pi r^2=\pi (10{)}^2=100\pi sq.cm$