R S Aggarwal and Veena Aggarwal Solutions for Exercise 2: Exercise 8B

In the given figure common tangents $\mathrm{AB}$ and $\mathrm{CD}$ to the two circles with centres ${\mathrm{O}}_1$ and ${\mathrm{O}}_2$ intersect at $\mathrm{E}$. Prove that $\mathrm{AB}=\mathrm{CD}$.

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Two concentric circles are of radii $5\mathrm{cm}$ and $3\mathrm{cm}$. Find the length of the chord of the larger circle (in $\mathrm{cm}$) which touches the smaller circle.

In the given figure, two tangents $\mathrm{RQ}$, and $\mathrm{RP}$ are drawn from an external point $\mathrm{R}$to the circle with centre $\mathrm{O}$. If $\angle \mathrm{PRQ}=120°$ , then prove that$\mathrm{OR}=\mathrm{PR}+\mathrm{RQ}$.

In the given figure, $\mathrm{O}$ is the centre of the circle. $\mathrm{PA}$ and $\mathrm{PB}$ are tangents. Show that $\mathrm{AOBP}$ is cyclic quadrilateral.

In two concentric circles, a chord of length $8 \mathrm{cm}$ of the large circle touches the smaller circle. If the radius of the larger circle is $5 \mathrm{cm}$ then find the radius of the smaller circle.

In the given figure, $PQ$ is chord of a circle with centre $O$and $PT$ is a tangent. If
$\angle QPT=60°$, find the $\angle PRQ$.

In the given figure, $\mathrm{PA}$ and $\mathrm{PB}$ are two tangents to the circle with centre $\mathrm{O}$. If $\angle \mathrm{APB}=60°$, then find the measure of $\angle \mathrm{OAB}$.

If the angle between two tangents drawn from an external point $P$ to a circle of radius $a$ and centre $O$, is $60°$ then find the length of $OP$.