All the vertices of a rhombus lie on a circle. Find the area of the rhombus, if the area of the circle is 1256 cm2. (Use π = 3.14)
Given that the area of the circle is 1256 cm2.
`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,
AD2 + CD2 = AC2
`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 AD2 is the area of the square.
Thus area of the square is 800cm2