Let $G$ be the centroid of the triangle $ABC$ in which the angle $C$ is obtuse. Let $AD$ and $CF$ are the medians from $A$ and $C$ on the sides $BC$ and $AB$ respectively. If the four points $B,D,G$ and $F$ are concyclic, then $\frac{BC}{AC}$

Let $ABCD$ be a square of side $20 cm$. The area of the square $PQRS$ (in $c{m}^2$) interior to $ABCD$, shown in the figure is

In the given figure, $ABCD$ is a rectangle. Then the area of the shaded region is

In quadrilateral $ABCD$, $\angle ABC+\angle DCB=90°$ and $ADEF$ is a square constructed on side $AD$ in the exterior of the quadrilateral $ABCD$. If $BC=10 \mathrm{cm},AC=9 \mathrm{cm}\text{ and }BD=8 \mathrm{cm}$, then the area (In ${\mathrm{cm}}^2$) of the square $ADEF$ lies between.