A sharpened pencil end point dot gives us an idea of a .

In $∆\mathrm{PQR}, \angle \mathrm{Q}>\angle \mathrm{R}, \mathrm{PS}$ is the bisector of $\angle \mathrm{P}$, and $\mathrm{PT}\perp \mathrm{QR}$. If $\angle \mathrm{SPT}={28}^{°}$ and $\angle \mathrm{R}={23}^{°}$, then the measure of $\angle \mathrm{Q}$ is:

In the triangle given above, $\angle \mathrm{ADB}={90}^{\mathrm{o}}, \angle \mathrm{ABC}={45}^{\mathrm{o}}, \mathrm{AD}=10 \mathrm{cm}, \mathrm{AC}=20 \mathrm{cm}.$ The length of $\mathrm{BC}$ is:

The wheels of a car are of diameter $80 \mathrm{c}\mathrm{m}$ each. How many complete revolutions does each wheel make in 10 minutes when the car is traveling at a speed of $66 \mathrm{k}\mathrm{m}$ per hour? $\left(\mathrm{use} \pi =\frac{22}{7}\right)$

In the given figure, $AB\parallel CD, \angle ABO=40°$ and $\angle CDO=35°$. Then the value of $x$ will be

Only one circle can be drawn through three non collinear points.

In $△ABC, AD$ is the median and $G$ is a point on $AD$ such that $AG:GD=2:1$. Then area $(△BDG):$area $(△ABC)$ is equal to: