Question

In fig. OPQR is a rhombus, three of whose vertices lie on the circle with centre O. If the area of the rhombus is $50\ast$ underoot3 cm sq., find the radius of the circle. Also, find the area of the sector ROPMR

Answer 1

Area of Rhombus $=\frac{1}{2}{d}_1{d}_2$
$=\frac{1}{2}=PR\times OQ=\frac{1}{2}=PR\times rLetPR\&OQintersectatx\therefore OQ=Q\times \frac{1}{2}rR{X}^2+O{x}^2=O{R}^{2}R{x}^2=O{R}^2-O{x}^2-r^2-(\frac{r}{2}{)}^2=\frac{3r^2}{4}\therefore Rr=\frac{\sqrt{3}}{2}rorPR=\sqrt{3}r\therefore A=\frac{1}{2}\times \sqrt{3}r\times r=50\sqrt{\text{/}3}or{r}^2=100r=10cm$
For area of sector ROPMR, Please specify where in r. Figure is not enclosed