R.K. Singh Solutions for Chapter: Geometry, Exercise 1: Model Questions

In $∆\mathrm{ABC}$ the medians $\mathrm{BE}$ and $\mathrm{CF}$ intersect at point $\mathrm{G}$. If the straight line $\mathrm{AGD}$, intersect $\mathrm{BC}$ at point $\mathrm{D}$ such that $\mathrm{GD}=1.5 \mathrm{cm}$ then the length of $\mathrm{AD}$ is:

The interior bisector of $\angle \mathrm{B}$ and $\angle \mathrm{C}$ of $∆\mathrm{ABC}$ meet at point $\mathrm{O}$. If $\angle \mathrm{A}=80°$, then the value of $\angle \mathrm{BOC}$ is:

In the following figure the area of the equilateral triangle inscribed in the square of side $\text{'}\mathrm{a}\text{'}$ will be:

The ratio of the internal and the external angle of a regular polygon is $2:1$. The number of the sides of the polygon is:

In an isosceles $∆\mathrm{ABC}$, a perpendicular is drawn through the point $\mathrm{P}$ on $\mathrm{BC}$, it intersect $\mathrm{AB}$ at $\mathrm{Q}$, and meet $\mathrm{CA}$ at $\mathrm{R}$ when $\mathrm{CA}$ is produced to $\mathrm{R}$. then:

If $\mathrm{PL}, \mathrm{QM}$ and $\mathrm{RN}$ are altitudes of $∆\mathrm{PQR}$ If $\mathrm{O}$ is the orthocentre of $∆\mathrm{PQR}$, then $\mathrm{Q}$ will be the ortho centre of:

$\mathrm{ABCD}$ is a parallelogram. If $\mathrm{E}$ and $\mathrm{F}$ are two points on sides $\mathrm{DC}$ and $\mathrm{AD}$ respectively. If areas of $∆\mathrm{AFB}$ and $\mathrm{\Delta BFC}$ are ${\mathrm{\Delta }}_1$ and ${\mathrm{\Delta }}_2$ respectively, then:

The vertex $\mathrm{A}$ of a vertical pillar is at the ground. $\mathrm{C}$ is the mid point of $\mathrm{AB}$. $\mathrm{BC}$ subtends an angle $\mathrm{\alpha }$ at point $\mathrm{P}$ on the ground. If $\mathrm{AP}=\mathrm{n}.\mathrm{AB}$, then $\tan \mathrm{\alpha }$ is: