Abhijit Guha Solutions for Chapter: Geometry, Exercise 1: Practice Problems Level 1

Find $x$, if $\mathrm{AB}$ is a secant and $\mathrm{BQ}$ is a tangent to circle:

The length of the tangent from $P$ to the circle is:

Find $x$. if $\mathrm{OA}$ and $\mathrm{OB}$ are tangents to the circle, $\angle CAB=90°$ and $\angle CBO=90°$.

$AC$ is a tangent to the circle $\mathrm{O}$. The value of $p°$ in terms of $\mathrm{q}°$.

If $\mathrm{PC}$ and $\mathrm{PD}$ are tangents to the circle from point $\mathrm{P}$ and $\mathrm{AB}$ is a third tangent at point $\mathrm{Q}$ such that $\mathrm{AQ}=3 \mathrm{cm}$ and $\mathrm{PC}=12 \mathrm{cm}$, then $\mathrm{PA}$ is:

If $\mathrm{PC}$ and $\mathrm{PD}$ are tangents to the circle from point $\mathrm{P}$ and $\mathrm{AB}$ is a third tangent at point $\mathrm{Q}$ such that $\mathrm{AQ}=3 \mathrm{cm}$ and $\mathrm{PC}=12 \mathrm{cm}$.

If $\mathrm{PQ}$ and $\mathrm{PR}$ are two tangents to a circle with centre $\mathrm{O}$ such that $\mathrm{POQ}=130°$ then $\angle \mathrm{RPQ}$:

In right $∆\mathrm{ABC}, \angle \mathrm{B}=90°, \mathrm{BC}=8 \mathrm{cm}. \mathrm{AB}=15 \mathrm{cm}$, then find the radius $\mathrm{r}$ of the circle.