question_answer

Find the area of a rhombus whose 3 vertices lie on the circumference of a circle and one vertex lies on the centre of circle of radius 7 cm.

A)  \[49\,c{{m}^{2}}\]                 

B)  \[\frac{49}{2}c{{m}^{2}}\]

C)  \[\frac{49\sqrt{3}}{2}c{{m}^{2}}\]                 

D)  \[49\sqrt{3}\,c{{m}^{2}}\]

Correct Answer: C

Solution :

   Let ABCO is a rhombus whose 3 vertices A, B and C lie on circumference of circle and one vertex lies on center. \[\therefore \]  \[BO=OC=AO=7\text{ }cm\] (Radius of circle) \[AB=BC=7cm\] (Sides of rhombus) \[\because \]   Figure formed two equilateral triangles. \[\therefore \]  Area of rhombus = 2 \[\times \] area of equilateral triangle. \[=2\,\times \frac{\sqrt{3}}{4}\times 7\times 7=\underline{\frac{\mathbf{49}\sqrt{\mathbf{3}}}{\mathbf{2}}\,\mathbf{c}{{\mathbf{m}}^{\mathbf{2}}}}\]