Suppose you are given a circle. Describe a method by which you can find the center of this circle.
Question types
Circle question types
56 questions across 3 question groups — pick any mix to generate a MATHEMATICS paper with step-by-step answer keys.
56
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3
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5
Question types
Sample Questions
Circle questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
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Draw two circles of different radii. How many points these circles can have in common? What is the maximum number of common points?
In the following figure, the line $\text{ABCD}$ is perpendicular to $PQ;$ where $P$ and $Q$ are the centers of the circles.
Show that:$(i) AB = CD ;(ii) AC = BD.$
View full solution →Show that:$(i) AB = CD ;(ii) AC = BD.$
The figure shows two concentric circles and $AD$ is a chord of a larger circle.
Prove that: $AB = CD.$
View full solution →Prove that: $AB = CD.$
The figure given below shows a circle with center $O$ in which diameter $AB$ bisects the chord $CD$ at point $E$. If $CE = ED = 8 \ cm$ and $EB = 4 \ cm,$
find the radius of the circle.
View full solution →find the radius of the circle.
In the given figure, $\text{AOC}$ is the diameter of the circle, with centre $O$. If arc $\text{AXB}$ is half of arc $\text{BYC}$, find $\angle BOC.$
View full solution →In the given figure, $O$ is the center of the circle with radius $20 \ cm$ and $OD$ is perpendicular to $AB$. If $AB = 32 \ cm,$
find the length of $CD.$
View full solution →find the length of $CD.$
In a circle of radius $10 \ cm, AB$ and $CD$ are two parallel chords of lengths $16 \ cm$ and $12 \ cm$ respectively.
Calculate the distance between the chords, if they are on:$(i)$ the same side of the center.$(ii)$ the opposite sides of the center.
View full solution →Calculate the distance between the chords, if they are on:$(i)$ the same side of the center.$(ii)$ the opposite sides of the center.
Prove that equal chords of congruent circles subtend equal angles at their center.
The radius of a circle is $13 \ cm$ and the length of one of its chords is $24 \ cm$.Find the distance of the chord from the center.
View full solution →In the given figure, $AB$ and $CD$ are two equal chords of a circle, with centre $O$. If $P$ is the mid$-$point of chord $AB, Q$ is the mid$-$point of chord $CD$ and $\angle POQ = 150^\circ ,$ find $\angle APQ.$
View full solution → Given two equal chords $AB$ and $CD$ of a circle with center $O$, intersecting each other at point $P.$Prove that:$(i) AP = CP;(ii) BP = DP$
View full solution →The circumference of a circle, with center $O$, is divided into three arcs $\text{APB, BQC}$, and $\text{CRA}$ such that:$\frac{\operatorname{arc} APB }{2}=\frac{\operatorname{arc} BQC }{3}=\frac{\operatorname{arc} CRA }{4}$Find $\angle BOC.$
View full solution →In the given figure, $AB = BC = DC$ and $\angle AOB = 50^\circ .(i) \angle AOC,(ii) \angle AOD,(iii) \angle BOD,(iv) \angle OAC,(v) \angle ODA$
View full solution → In the given figure, the lengths of arcs $AB$ and $BC$ are in the ratio $3:2.$ If $\angle AOB = 96^\circ $,find: $(i) \angle BOC ;(ii) \angle ABC$
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