**Areas related to Circles ncert solutions Chapter 12 Exercise 12.3 Question 6**

**6.** In a circular table cover of radius 32 cm, a design is formed leaving an equilateral triangle ABC in the middle as shown in the diagram. Find the area of the design.

**Given: **ABC is an equilateral triangle inscribed in circle of radius **32 cm**.

**Construction: **Draw AD BC, OE AB and OF AC.

In and

AC=AB {Sides of Equilateral triangle}

AD=AD {Common side}

Therefore, by RHS ,

Therefore, {Corresponding angles of congruent triangles are equal} **(1)**

And, we have **(2)**

{ is an equilateral triangle}

From **(1) and (2), **we have

Now, in

**cm**

Similarly, we have **cm**

Therefore, we have side AB of equilateral

**cm**

Area of Equilateral

Area of Design= Area of circle-Area of Equilateral triangle=