This is question no 7 page number 96 from following link https://tstuition.wikispaces.com/file/view/3+-+Mensuration.pdf Many many thanks

We'll have to determine the length of the side of
equilateral triangle to determine then it's area.

We know
that the radius of the circle is of 10 cm.

If we'll join
the center of the circle with 2 vertices of triangle, we'll get an isosceles triangle.
Since the inscribed angle of equilateral triangle measures 60 degrees, then the
corresponding central angle (which is the included angle between the two radii that are
the legs of the isosceles triangle) measures 2*60 = 120
degrees.

We'll draw the height of the isosceles triangle
that falls in the midpoint of the base of this triangle, base that is one of the legs of
the equilateral triangle.

This height bisects the angle of
120. We'll get the right angle triangle, whose hypotenuse is the radius of
circle.

We'll use the sine function to get the length of
half of the leg of equilateral triangle:

sin 60 =
x/10

`sqrt(3)` /2 =
x/10

`sqrt(3)` = x/5

x =
5`sqrt(3)`

The length of each side of equilateral triangle
measures 10`sqrt(3)` cm.

Now, we'll get the area of
equilateral triangle;

A = 10`sqrt(3)` *10`sqrt(3)` *sin
60/2

A = 150`sqrt(3)` /2

A =
75`sqrt(3)` `cm^(2)`

Now, to get the area of the shaded
region, we'll subtract the area of equilateral triangle from the area of the
circumscribed circle.

The area of the circle
is:

S = `pi` *`10^(2)`

S = 100
`pi` `cm^(2)`

Therefore, the area of the
equilateral triangle is A = 75`sqrt(3)` `cm^(2)` and the area of the shaded region is S
- A = (100`pi` - 75`sqrt(3)` ) `cm^(2)` .