Abhijit Guha Solutions for Chapter: Geometry, Exercise 3: Exam Problems

Find the value of $x$:

In the given figure $\mathrm{AB}\Vert \mathrm{DC}$ and $\mathrm{DE}\Vert \mathrm{BF}$, then the value of $x$ is:

Given that $\mathrm{ABC}=90°, \mathrm{BC}$ is parallel to $\mathrm{DE}$. If $\mathrm{AB}=12 \mathrm{cm}, \mathrm{BD}=6 \mathrm{cm}$ and $\mathrm{BC}=10 \mathrm{cm}$, then $\mathrm{DE}$ is:

If $G$ be the centroid of $∆ABC$ and the area of $∆GBD$ is $6 {\mathrm{cm}}^2$, where $D$ is the midpoint of the side $BC$, then the area of $∆ABC$ will be-

$\mathrm{D}$ is any point on side $\mathrm{AC}$ of $∆\mathrm{ABC}$. If $\mathrm{P}, \mathrm{Q}, \mathrm{X}, \mathrm{Y}$ are the mid points of $\mathrm{AB}, \mathrm{BC}, \mathrm{AD}$ and $\mathrm{DC}$ respectively, then the ratio of $\mathrm{PX}$ and $\mathrm{QY}$ is:

The length of the common chord of two circles of radii $30 \mathrm{cm}$ and $40 \mathrm{cm}$ whose centres are $50 \mathrm{cm}$ apart is:

If $\mathrm{O}$ be the circumcentre of a triangle $\mathrm{PQR}$ and $\mathrm{QOR}=110°\angle \mathrm{OPR}=25°$, then the measure of $\angle \mathrm{PRQ}$ is:

In $∆\mathrm{ABC}, \angle \mathrm{A}=\angle \mathrm{B}=60°, \mathrm{AC}=\sqrt{13}$. The lines $\mathrm{AD}$ and $\mathrm{BD}$ intersect at $\mathrm{D}$ with $\angle \mathrm{D}=90°$, if $\mathrm{DB}=2 \mathrm{cm}$, then the length of $\mathrm{AD}$ is: