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
If $1+\sin^2(2A)=3\sin A\cos A$, then what are the possible values of $\tan A$?
If \[ 2\sin\alpha + 15\cos^{2}\alpha = 7, \quad 0^\circ < \alpha < 90^\circ, \] find \(\cot\alpha\).
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
At the end of a business conference, the ten people present all shake hands with each other once. How many handshakes will there be altogether?
In the Adjoining figure, if O is the centre of the circle of radius 5cm, OP=13 cm, where PQ and PR are tangents to the circle from point P. Length PR is :
In the Adjoining figure DE \(||\) BC and \(\frac{\text{AD}}{\text{DB}} = \frac{3}{5}\) if AC = 4.8 cm. Then AE equals :
