All the vertices of a rhombus lie on a circle. Find the area of the rhombus, if the area of the circle is 1256 cm^{2}. (Use π = 3.14)

#### Solution

Given that the area of the circle is 1256 cm^{2}.

`pir^2 = 12563.14 xx r^2`

`3.14xxr^2 = 1256`

`r^2 = 1256/3.14`

`r^2 = 400`

r = 20 cm

If all the vertices of a rhombus lie on a circle, then the rhombus is square.

Consider the following figure.

Here A, B, C and D are four points on the circle.

Thus, OA = OB = OC = OD = radius of the circle.

⇒ AC and BD are the diameters of the circle.

Consider the Δ ADC.

By Pythagoras theorem, we have,

AD^{2} + CD^{2} = AC^{2}

`2AD^2 = (2 xx 20)^2` ......[AD = CD]

`2AD^2 = (40)^2`

`AD^2 = 1600/2`

`AD^2 = 800 cm^2`

If AD is the side of the square, then AD^{2} is the area of the square.

Thus area of the square is 800cm^{2}