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 p = 3.14]

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#### Solution

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

`pir^2=12563.14xxr^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=(2x20)^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}

Concept: Circumference of a Circle

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