Question types
Circles question types
374 questions across 9 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.
374
Questions
9
Question groups
5
Question types
01
M.C.Q
249 Q→02Assertion (A) & Reason (B) MCQ
61 Q→03True False[1 Marks ]
18 Q→04Fill In The Blanks[1 Marks ]
9 Q→051 Marks Question
3 Q→062 Marks Questions
9 Q→073 Marks Question
10 Q→085 Marks Questions
7 Q→09Case study (4 Marks)
8 Q→Sample Questions
Circles questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
A chord of length $14\ cm$ is at a distance of $6\ cm$ from the centre of a circle. The length of another chord at a distance of $2\ cm$ from he centre of the circle is:
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In the give figure, ABCD is a cyclic quadrilateral in which BC = CD and $\angle\text{CBD}=35^\circ.$ Then, $\angle\text{BAD}=?$
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Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: Sector is a region of a circle between the arc and the two radii of the circle.
Reason: Sector is the region between the chord and its corresponding arc.
Assertion: Sector is a region of a circle between the arc and the two radii of the circle.
Reason: Sector is the region between the chord and its corresponding arc.
- Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- Assertion is true but the reason is false.
- Both assertion and reason are false.
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: Given a circle of radius r and with centre O. A point P lies in a plane such that OP > r then point P lies on the exterior of the circle.
Reason: The region between an arc and the two radii, joining the centre of the end points of the arc, is called a sector.
Assertion: Given a circle of radius r and with centre O. A point P lies in a plane such that OP > r then point P lies on the exterior of the circle.
Reason: The region between an arc and the two radii, joining the centre of the end points of the arc, is called a sector.
- Both assertion and reason are true and reason is the correct enatixplaon of assertion.
- Both assertion and reason are true but reason is not the correct explanation of assertion.
- Assertion is true but reason is false.
- Assertion is false but reason is true.
Directions: In the following questions, the Assertions (A) and Reason(s) (R) have been put forward. Read both the statements carefully and choose the correct alternative from the following:
Assertion: Rectangle is a cyclic quadrilateral.
Reason: Their vertices lies on the circumference of a circle.
Assertion: Rectangle is a cyclic quadrilateral.
Reason: Their vertices lies on the circumference of a circle.
- Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
- Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.
- Assertion is true but the reason is false.
- Both assertion and reason are false.
If $\text{AOB}$ is a diameter of a circle and $C$ is a point on the circle, then $AC^2 + BC^2 = AB^2.$
View full solution →ABCD is a cyclic quadrilateral such that $\angle\text{A}=90^\circ,\angle\text{B}=70^\circ,\angle\text{C}=95^\circ$ and $\angle\text{D}=105^\circ.$
View full solution →The degree measure of a semi-circle is 180°
A circle is a plane figure.
If A, B, C, D are four points such that $\angle\text{BAC}=30^\circ$ and $\angle\text{BDC}=60^\circ$ then D is the centre of the circle through A, B and C.
View full solution →A point whose distance from the center of a circle is greater than its radius lies in __________ of the circle.
All points lying inside/outside a circle are called ________ points/ _________ points.
Segment of a circle is a region between an arc and _________ of the circle.
Circle having the same centre and different radii are called _________ circles.
The longest chord of a circle is a __________ of the circle.
In figure, A, B, C, D are four points on the circle. AC and BD intersect at a point E such that $\angle$BEC = 130° and $\angle$ECD = 20° Find $\angle$BAC.
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In Fig., $\text{ABCD}$ is a cyclic quadrilateral in which $AC$ and $BD$ are its diagonals. If $\angle DBC = 55^\circ$ and $\angle BAC = 45^\circ , $find $\angle BCD.$
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In given figure, $\angle ABC = 69^\circ , \angle ACB = 31^\circ ,$ find $\angle BDC.$
View full solution →A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the minor arc and also at a point on the major arc.
If circles are drawn taking two sides of a triangle as diameters, prove the point of intersection of these circles lie on the third side.
In figure, $\text{A, B, C}$ are three points on a circle with centre $O$ such that $\angle BOC = 30^\circ \angle AOB = 60^\circ$ . If $D$ is a point on the circle other than the arc $\text{ABC},$ find $\angle ADC.$
View full solution →Equal chords of a circle (or of congruent circles) are equidistant from the centre (or centres)
The line drawn through the centre of a circle to bisect a chord is perpendicular to the chord
Equal chords of a circle subtend equal angles at the centre.
If two non - parallel sides of a trapezium are equal, prove that it is cyclic.
$\text{ABCD}$ is a cyclic quadrilateral whose diagonals intersect at a point $E$. If $\angle DBC = 70^\circ$ $\angle BAC$ is $30^\circ,$ find $\angle BCD. $ Further, if $AB = BC,$ find $\angle BCD$. If $AB = BC,$ find $\angle ECD.$
View full solution →If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral, prove that it is a rectangle.
In figure, $\angle \mathrm { PQR } = 100 ^ { \circ }$, where $P, Q$ and $R$ are points on a circle with centre $O.$ Find $\angle O P R$
View full solution →The circular park of radius $20 m$ is situated in a colony. Three boys Ankur, Syed and David are sitting at equal distance on its boundary each having a toy telephone in his hands to talk each other. Find the length of the string of each phone.
View full solution →Three girls Reshma, Salma and Mandip are playing a game by standing on a circle of radius $5 m$ drawn in a park. Reshma throws a ball to Salma. Salma to Mandip, Mandip to Reshma. If the distance between Reshma and Salma and between Salma and Mandip is 6 m each, what is the distance between Reshma and Mandip?
View full solution →If two equal chords of a circle intersect within a circle, prove that the segments of one chord are equal to corresponding segments of the other chord.
Read the Source/ Text given below and answer any four questions:
Four students of class $IX B$ with names Ajay, Babloo, Charan and Deepak are playing a game in a circular playground. All four students are holding radios with speaker and mic. These radios are connected by a wire of equal length that is $11\ m ($for each radio$).$ Ajay Asks a question to Babloo. If Babloo gives the correct answer he gets $10$ points and asks a new question to Charan, If he can not answer then he passes the same question to Charan and gets no points. These conditions apply to all four players. After $10$ rounds who gets maximum points, he becomes the winner.
View full solution →Four students of class $IX B$ with names Ajay, Babloo, Charan and Deepak are playing a game in a circular playground. All four students are holding radios with speaker and mic. These radios are connected by a wire of equal length that is $11\ m ($for each radio$).$ Ajay Asks a question to Babloo. If Babloo gives the correct answer he gets $10$ points and asks a new question to Charan, If he can not answer then he passes the same question to Charan and gets no points. These conditions apply to all four players. After $10$ rounds who gets maximum points, he becomes the winner.
- What is the radius of the field?
- $7\ m$
- $14\ m$
- $11\ m$
- $22\ m$
- What is the area of the field?
- $70\ m^2$
- $154\ m^2$
- $110\ m^2$
- $220\ m^2$
- What is the area of the part marked with $1$ on the field?
- $50\ m^2$
- $154\ m^2$
- $76\ m^2$
- $38.5\ m^2$
- What is the circumference of the field?
- $22\ m$
- $14\ m$
- $44\ m$
- $28\ m$
- What is the direct distance from Ajay to Charan?
- $7\ m$
- $28\ m$
- $15\ m$
- $14\ m$
Two new roads, Road E and Road F were constructed between society 4 and 1 and society 1 and 2.
5. What would be the measure of the sum of angles formed by the straight roads at society 1 and society 3?
A. 60°
B. 90°
C. 180°
D. 360°
6. Krish says, “The distance to go from society 4 to society 2 using Road D will be longer that the distance using Road E”
Is Krish correct? Justify your answer with examples.
7. Road G, perpendicular to Road F was constructed to connect the park and Road F.
Which of the following is true for Road G and Road F?
A. Road G and road F are of same length.
B. Road F divides Road G into two equal parts.
C. Road G divides Road F into two equal parts.
D. The length of road G is one-fourth of the length of Road F.
8. Priya said, “Minor arc corresponding to Road B is congruent to minor arc corresponding to Road D.”
Do you agree with Priya? Give reason to support your answer.
Given below is the map giving the position of four housing societies in a township connected by a circular road A.
Society 2 and 3 are connected by straight road B, society 4 and 2 are connected by straight road C and society 4 and 3 are connected by road D. Point P denotes the position of a park. The park is equidistant to all four societies.
Rubina claims that it is not possible to construct another circular road connecting all four societies.
1. Which of the following options justiies Rubina’s claim?
A. Equal chords of congruent circles subtend equal angles at the centre.
B. The perpendicular from the centre of a circle to a chord bisects the chord.
C. There is a unique circle passing through three non-collinear points.
D. Points equidistant from a given point will lie on a circle.
2 What is the position of the park P with respect to road A?
A. Chord
B. Centre
C. Sector
D. Segment
3. The length of Road B is equal to the length of Road D.
Which of the following options can be true for the roads in the township?
A. Road B bisects Road D.
B. Road B and Road make an acute angle.
C. Road B, Road C and Road D are of equal length.
D. Road B and Road D subtend equal angles at society 1.
4. Alex says, “The angle made by road B on road D is a right angle.”
Jai and Angad give different justiications to support Alex’s claim.
Jai says, “Angles in the same segment of a circle are equal.”
Angad says, “The angle in a semicircle is a right angle.”
Who has given the correct justiication?
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