R. D. Sharma Solutions for Chapter: Circles, Exercise 4: MULTIPLE CHOICE QUESTIONS (MCQs)

In the given figure, a circle touches the side $\mathrm{DF}$ of $△\mathrm{EDF}$ at $\mathrm{H}$ and touches $\mathrm{ED}$ and $\mathrm{EF}$ produced at $\mathrm{K}$ and $\mathrm{M}$ respectively. If $\mathrm{EK}=9 \mathrm{cm}$, then the perimeter of $△\mathrm{EDF}$ is

A quadrilateral $\mathrm{ABCD}$ is drawn to circumscribe a circle such that its sides $\mathrm{AB}, \mathrm{BC}, \mathrm{CD}$ and $\mathrm{AD}$ touch the circle at $\mathrm{P}, \mathrm{Q}, \mathrm{R}$ and $\mathrm{S}$ respectively. If $\mathrm{AB}=x \mathrm{cm}, \mathrm{BC}=7 \mathrm{cm}, \mathrm{CR}=3 \mathrm{cm}$ and $\mathrm{AS}=5 \mathrm{cm}$, then $x=$_____ $\mathrm{cm}$

At one end $\mathrm{A}$ of a diameter $\mathrm{AB}$ of a circle of radius $5 \mathrm{c}\mathrm{m}$, tangent $\mathrm{XAY}$ is drawn to the circle. The length of the chord $\mathrm{CD}$ parallel to $\mathrm{XY}$ and at a distance $8 \mathrm{c}\mathrm{m}$ from $\mathrm{A}$ is

From a point $\mathrm{P}$ which is at a distance $13 \mathrm{c}\mathrm{m}$ from the centre $\mathrm{O}$ of a circle of radius $5 \mathrm{c}\mathrm{m},$ the pair of tangents $\mathrm{PQ}$ and $\mathrm{PR}$ to the circle are drawn. Then the area of the quadrilateral $\mathrm{PQOR}$ is

If $\mathrm{PA}$ and $\mathrm{PB}$ are tangents to the circle with centre $\mathrm{O}$ such that $\angle \mathrm{A}\mathrm{P}\mathrm{B}=50°,$ then $\angle \mathrm{O}\mathrm{A}\mathrm{B}$ is equal to

The pair of tangents $\mathrm{AP}$ and $\mathrm{AQ}$ drawn from an external point to a circle with centre $\mathrm{O}$ are perpendicular to each other and length of each tangent is $5 \mathrm{c}\mathrm{m}.$ The radius of the circle is

In figure, if $\mathrm{\angle }\mathrm{A}\mathrm{O}\mathrm{B}=125°$, then $\mathrm{\angle }\mathrm{DOC}$ is equal to

In the figure, if $\mathrm{PQR}$ is the tangent to a circle at $\mathrm{Q}$ whose centre is $\mathrm{O}$ , $\mathrm{AB}$ is a chord parallel to $\mathrm{PR}$ and $\mathrm{\angle }\mathrm{B}\mathrm{Q}\mathrm{R}\mathrm{}=\mathrm{}{70}^{°}$ then $\mathrm{\angle }\mathrm{A}\mathrm{Q}\mathrm{B}$ is equal to

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