SSC
Sample Paper
SSC CHSL (10+2) Sample Test Paper-23
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. \[=2\,\times \frac{\sqrt{3}}{4}\times 7\times 7=\underline{\frac{\mathbf{49}\sqrt{\mathbf{3}}}{\mathbf{2}}\,\mathbf{c}{{\mathbf{m}}^{\mathbf{2}}}}\]