In the given figure, $ABCD$ is a rectangle. $P$ and $Q$ are the midpoints of sides $CD$ and $BC$ respectively. Then the ratio of area of shaded portion to the area of unshaded portion is:
In the adjoining figure, points $A,B,C,D$ lie on a circle. $AD=24$ and $BC=12$. What is the ratio of the area of $\triangle CBE$ to that of $\triangle ADE$?
In $\triangle ABC$, $D$ is a point on $BC$ such that $3BD=BC$. If each side of the triangle is $12\,$cm, then $AD$ equals
In the figure, $\triangle APB$ is formed by three tangents to a circle with centre $O$. If $\angle APB=40^\circ$, then the measure of $\angle BOA$ is
In an equilateral triangle $ABC$, if the area of its in-circle is $4\pi\ \text{cm}^2$, then find the length of the angle bisector $AD$?
