Abhijit Guha Solutions for Chapter: Geometry, Exercise 2: Practice Problems Level 2

In a triangle $\mathrm{ABC}$, the lengths of the sides $\mathrm{AB} , \mathrm{AC}$ and $\mathrm{BC}$ are $3 , 5$ and $6\mathrm{cm}$ respectively. If a point $\mathrm{D}$ on $\mathrm{BC}$ is drawn such that the line $\mathrm{AD}$ bisects the $\angle \mathrm{A}$ internally, then what is the length of $\mathrm{BD}$?

If $ABCD$ is a rectangle, $E, F$ are the mid-point of $BC$ and $AD$respectively and $G$is any point on $EF$, then $\Delta GAB$ equals.

In the given figure $∆\mathrm{PST}~∆\mathrm{PQR}$,

if $\frac{\mathrm{PR}}{\mathrm{QR}}=\frac{3}{2}$, then $\mathrm{ST}:\mathrm{PT}$ is:

If $\mathrm{O}$ is the centre of the circle, and $\mathrm{XAY}$ is a tangent to the circle.

If $\angle \mathrm{BAX}=80°, \angle \mathrm{BAQ}=50°$, then value of $\mathrm{x}$ is:

Triangle PQR circumscribes a circle with centre O and radius r cm such that  \( \angle\;PQR=90^0 \) . If  PQ=3 cm, QR=4 cm, then the value of r is:

The largest angle of a triangle of sides $17 \mathrm{cm}, 13 \mathrm{cm}$ and $10 \mathrm{cm}$ is:

Given inside a circle, of radius $13 \mathrm{cm}$, point $P$ is at a distance of $5 \mathrm{cm}$ form the centre $O$. A chord $XY$ of $25 \mathrm{cm}$ is drawn through $\mathrm{P}$, then $\frac{XP}{YP}$ is:

There is a triangle with sides of any positive integer having area ${\mathrm{T}}_1$. Three squares are drawn on each side of triangle. The area of the squares ${\mathrm{S}}_1, {\mathrm{S}}_2$ and ${\mathrm{S}}_3$. What is the value of $\mathrm{A}$ if $\mathrm{A}={\mathrm{T}}_1+{\mathrm{S}}_1+{\mathrm{S}}_2+{\mathrm{S}}_3$.