Question

an equilateral triangle is inscribed  in a circle of radius 10cm find area of triangle

Answer 1

triangle is equilateral

tan30=1/root3

=x/10

therefore x=10 root3

area = 6 * area of right angle triangle

area = 6* 1/2*10 root 3* 10

area =300 root 3

Answer 2

let ABC be the equilateral triangle and circle with centre O touching triangle at point P,Q and R.
join OR.
Now in triangle OQC 
tan30=OQ/QC     =   1/√3=10/QC
=QC=10√3
and BC=20√3
area of equilateral triangle=√3/4*a²
                                     =√3/4*20√3*20√3
                                     =300√3cm²