If the length of a chord of a circle is $16\ cm$ and is at a distance of $15\ cm$ from the centre of the circle, then the radius of the circle is:
- A$15\ cm.$
- B$16\ cm.$
- ✓$17\ cm.$
- D$34\ cm.$
Answer: C.
View full solution →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
MCQ(1M)
29 Q→02Fill in the Blanks.
8 Q→03True False With Reason
8 Q→042 Mark Question
2 Q→053 Mark Question
25 Q→064 Mark Question
47 Q→075 Mark Question
6 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.
In the given figure, if $\angle\text{ABC} = 45^\circ,$ then $\angle\text{AOC} =$
- A$45^\circ$
- B$60^\circ$
- C$75^\circ$
- ✓$90^\circ$
Answer: D.
View full solution →$\text{ABC}$ is a triangle with $B$ as right angle, $AC = 5\ cm$ and $AB = 4\ cm$. A circle is drawn with $A$ as centre and $\text{AC}$ as radius. The length of the chord of this circle passing through $C$ and $B$ is:
- A$3\ cm.$
- B$4\ cm.$
- C$5\ cm.$
- ✓$6\ cm.$
Answer: D.
View full solution →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 $\angle\text{ABC} =$
- A$60^\circ$
- ✓$75^\circ$
- C$90^\circ$
- D$135^\circ$
Answer: B.
View full solution →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 →Fill in the blanks:
A circle divides the plane, on which it lies, in _________ parts.
A circle divides the plane, on which it lies, in _________ parts.
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:
The longest chord of a circle is a __________ of the circle.
The longest chord of a circle is a __________ of the circle.
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:
Line segment joining the center to any point on the circle is a radius of the circle,
Line segment joining the center to any point on the circle is a radius of the circle,
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.
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 two different circles cannot intersect each other at more than two points.
If O is the centre of the circle, find the value of x in the following figure:
In the given figure, O is the center of the circle. If $\angle\text{BOD}=160^\circ,$ find the value of x and y.
View full solution →If O is the centre of the circle, find the value of x in the following figures:
If O is the centre of the circle, find the value of x in the following figure:
Prove that the line joining the mid-point of a chord to the centre of the circle passes through the mid-point of the corresponding minor arc.
Suppose you are given a circle. Give a construction to find its centre.
Two chords AB, CD of lengths 5cm, 11cm respectively of a circle are parallel. If the distance between AB and CD is 3cm, find the radius of the circle.
In a cyclic quadrilateral ABCD, if $\angle\text{A}-\angle\text{C}=60^\circ,$ prove that the smaller of two is $60^{\circ}$
View full solution →In the given figure, ABCD is a quadrilateral inscribed in a circle with centre O. CD is produced to E such that $\angle\text{AED} = 95^\circ$ and $\angle\text{OBA} = 30^\circ$ Find $\angle\text{OAC.}$
View full solution →The radius of a circle is $8\ cm$ and the length of one of its chords is $12\ cm$. Find the distance of the chord from the centre.
View full solution →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 $\angle\text{CAO.}$
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