Number of circles that can be drawn through three non-collinear points is:
- 1
- 0
- 2
- 3
Question types
Circles question types
125 questions across 7 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.
125
Questions
7
Question groups
5
Question types
01
M.C.Q
29 Q→02True False[1 Marks ]
8 Q→03Fill In The Blanks[1 Marks ]
8 Q→042 Marks Questions
2 Q→053 Marks Question
25 Q→065 Marks Questions
6 Q→074 Marks Questions
47 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.
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In the given figure, if $\angle\text{ABC} = 45^\circ,$ then $\angle\text{AOC} =$
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- 45°
- 60°
- 75°
- 90°
If A , B, C are three points on a circle with centre O such that $\angle\text{AOB} = 90^\circ$ and $\angle\text{BOC} = 120^\circ,$ then $\angle\text{ABC} =$
View full solution →- 60°
- 75°
- 90°
- 135°
Two equal circles of radius $r$ intersect such that each passes through the centre of the other. The length of the common chord of the circle is:
- A$\sqrt{\text{r}}$
- B$\sqrt{2}\text{r}\text{AB}$
- ✓$\sqrt{3}\text{r}$
- D$\frac{\sqrt3}{2}$
Answer: C.
View full solution →The radius of a circle is $6\ cm$. The perpendicular distance from the centre of the circle to the chord which is $8\ cm$ in length, is:
- A$\sqrt{5}\text{cm}.$
- ✓$2\sqrt{5}\text{cm}.$
- C$2\sqrt{7}\text{cm}.$
- D$\sqrt{7}\text{cm}.$
Answer: B.
View full solution →Write the truth value (T/F) of the following with suitable reasons:
Sector is the region between the chord and its corresponding arc.
Sector is the region between the chord and its corresponding arc.
Write the truth value (T/F) of the following with suitable reasons:
If a circle is divided into three equal arcs each is a major arc.
If a circle is divided into three equal arcs each is a major arc.
Write the truth value (T/F) of the following with suitable reasons:
A circle has only finite number of equal chords.
A circle has only finite number of equal chords.
Write the truth value (T/F) of the following with suitable reasons:
A circle is a plane figure.
A circle is a plane figure.
Write the truth value (T/F) of the following with suitable reasons:
The degree measure of a semi-circle is 180°
The degree measure of a semi-circle is 180°
Fill in the blanks:
The longest chord of a circle is a __________ of the circle.
The longest chord of a circle is a __________ of the circle.
Fill in the blanks:
An arc is a __________ when its ends are the ends of a diameter.
An arc is a __________ when its ends are the ends of a diameter.
Fill in the blanks:
A point whose distance from the center of a circle is greater than its radius lies in __________ of the circle.
A point whose distance from the center of a circle is greater than its radius lies in __________ of the circle.
Fill in the blanks:
A continuous piece of a circle is _________ of the circle.
A continuous piece of a circle is _________ of the circle.
Fill in the blanks:
Segment of a circle is a region between an arc and _________ of the circle.
Segment of a circle is a region between an arc and _________ of the circle.
In the given figure, if $\angle\text{BAC}=60^\circ$ and $\angle\text{BCA}=20^\circ,$ find $\angle\text{ADC}.$
View full solution →In the given figure, $\triangle\text{ABC}$ is an equilateral triangle. Find $\text{m}\angle\text{BEC}.$
View full solution →Prove that the centre of the circle circumscribing the cyclic rectangle ABCD is the point of intersection of its diagonals.
If O is the centre of the circle, find the value of x in the following figure:
In the given figure, If ABC is an equilateral triangle. Find $\angle\text{BDC}$ and $\angle\text{BEC.}$
View full solution →If O is the centre of the circle, find the value of x in the following figure:
Prove that two different circles cannot intersect each other at more than two points.
In the given figure, ABCD is a cyclic quadrilateral in which $\angle\text{BAD} = 75^\circ,\ \angle\text{ABD} = 58^\circ$ and $\angle\text{ADC} = 77^\circ, $ AC and BD intersect at P. Then, find $\angle\text{DPC}.$
View full solution →In the given figure, AB is a diameter of the circle such that $\angle\text{A}=35^\circ$ and $\angle\text{Q}=25^\circ,$ find $\angle\text{PBR.}$
View full solution →In the given figure, A is the centre of the circle. ABCD is a parallelogram and CDE is a straight line. Find $\angle\text{BCD}:\angle\text{ABE}.$
View full solution →In the given figure, if $\angle\text{AOB} = 80^\circ$ and $\angle\text{ABC} = 30^\circ,$ then find $\angle\text{CAO.}$
View full solution →In the given figure, P and Q are centres of two circles intersecting at B and C. ACD is a straight line. Then, $\angle\text{BQD} =$
View full solution →Prove that the line segment joining the mid-point of the hypotenuse of a right triangle to its opposite vertex is half of the hypotenuse.
ABCD ia a cyclic quadrilateral in which BA and CD when produced meet in E and EA = ED. Prove that:
- AD || BC.
- EB = EC.
In the given figure, ABCD is a cyclic quadrilateral. Find the value of x.
If the two sides of a pair of opposite sides of a cyclic quadrilateral ae equal, prove that its diagonals are equal.
In a cyclic quadrilateral ABCD if $\text{m}\angle\text{A}=\big(\text{m}\angle\text{C}\big).$ Find $\text{m}\angle\text{A}.$
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