All the vertices of a rhombus lie on a circle | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the radius of the circle be $r$.Given that,Area of the circle $= 1256 \, cm^{2}$.$\pi r^{2} = 1256$$r^{2} = \frac{1256}{3.14} = 400$$r = \sqrt

Vedclass · Accepted Answer

$800$

Vedclass · Answer

(C) Let the radius of the circle be $r$.Given that,Area of the circle $= 1256 \, cm^{2}$.$\pi r^{2} = 1256$$r^{2} = \frac{1256}{3.14} = 400$$r = \sqrt{400} = 20 \, cm$.Since all the vertices of a rhombus lie on a circle,the rhombus must be a square because its diagonals are diameters of the circle and they bisect each other at $90^{\circ}$.Thus,the diagonals $d_{1}$ and $d_{2}$ are equal to the diameter of the circle.$d_{1} = d_{2} = 2 	imes r = 2 	imes 20 = 40 \, cm$.Area of the rhombus $= \frac{1}{2} 	imes d_{1} 	imes d_{2}$$= \frac{1}{2} 	imes 40 	imes 40$$= 20 	imes 40 = 800 \, cm^{2}$.Hence,the required area of the rhombus is $800 \, cm^{2}$.

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 $\pi = 3.14$). (in $cm^{2}$)

Similar Questions

Find the area of the flower bed (with semi-circular ends) shown in the figure.

The ratio of the areas of $\odot(O, 6)$ and $\odot(P, 12)$ is ...........

In the figure,a square is inscribed in a circle of diameter $d$ and another square is circumscribing the circle. Is the area of the outer square four times the area of the inner square? Give reasons for your answer.

In the figure,a circle is inscribed in a square of side $5 \, cm$ and another circle is circumscribing the square. Is it true to say that the area of the outer circle is two times the area of the inner circle? Give reasons for your answer.

The radius of a semicircular garden is $35 \, m$. One has to walk $\ldots \ldots \ldots \ldots \, m$ to make one complete round of that garden.

Vedclass Test Series

Exam Paper Generator

Online Exam Module