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
248 questions across 9 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
248
Questions
9
Question groups
5
Question types
01
M.C.Q
95 Q→02Assertion (A) & Reason (B) MCQ
14 Q→03True False[1 Marks ]
8 Q→04Fill In The Blanks[1 Marks ]
41 Q→051 Marks Question
10 Q→062 Marks Questions
2 Q→073 Marks Question
25 Q→085 Marks Questions
6 Q→094 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.
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 →$ABC$ is a triangle with $B$ as right angle, $AC = 5\ cm$ and $AB = 4\ cm$. A circle is drawn with $A$ as centre and $AC$ 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 →Statement-1 (A): In Fig.(i), if AOB is a diameter and $\angle A D C=120^{\circ}$, then $\angle C A B=30^{\circ}$.
Statement-2 (R): In Fig.(ii), AOB is a diameter and $\angle A D C=120^{\circ}$, then $\angle B A C=30^{\circ}$.
Statement-2 (R): In Fig.(ii), AOB is a diameter and $\angle A D C=120^{\circ}$, then $\angle B A C=30^{\circ}$.
- ✓Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
- BStatement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
- CStatement-1 is True, Statement-2 is False.
- DStatement-1 is False, Statement-2 is True.
Answer: A.
View full solution →Statement-1 (A): If A, B, C, D are four points such that $\angle B A C=30^{\circ}$ and $\angle B D C=60^{\circ}$, then D is the centre of the circle through A, B and C.
Statement-2 (R): The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.
Statement-2 (R): The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.
- AStatement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
- BStatement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
- CStatement-1 is True, Statement-2 is False.
- ✓Statement-1 is False, Statement-2 is True.
Answer: D.
View full solution →Statement-1 (A): A circle of radius 3 cm can be drawn through two points $A, B$ such that $A B=6 cm$.
Statement-2 (R): Through three collinear points a circle can be drawn.
Statement-2 (R): Through three collinear points a circle can be drawn.
- AStatement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
- BStatement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
- ✓Statement-1 is True, Statement-2 is False.
- DStatement-1 is False, Statement-2 is True.
Answer: C.
View full solution →Statement-1 (A): If A, B, C and D are four points such that $\angle B A C=45^{\circ}$ and $\angle B D C=45^{\circ}$, then A, B, C, D are concyclic.
Statement-2 (R): ABCD is a cyclic quadrilateral such that $\angle A=85^{\circ}, \angle B=70^{\circ}$, $\angle C=95^{\circ}$ and $\angle D=110^{\circ}$
Statement-2 (R): ABCD is a cyclic quadrilateral such that $\angle A=85^{\circ}, \angle B=70^{\circ}$, $\angle C=95^{\circ}$ and $\angle D=110^{\circ}$
- AStatement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
- ✓Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
- CStatement-1 is True, Statement-2 is False.
- DStatement-1 is False, Statement-2 is True.
Answer: B.
View full solution →Statement-1 (A): If AOB is a diameter of a circle and C is a point on the circle, then $A C^2+B C^2=A B^2$
Statement-2 (R): Angle is a semi-circle is a right angle.
Statement-2 (R): Angle is a semi-circle is a right angle.
- ✓Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
- BStatement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
- CStatement-1 is True, Statement-2 is False.
- DStatement-1 is False, Statement-2 is True.
Answer: A.
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.
View full solution →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.
View full solution →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,
View full solution →Write the truth value $(T/F)$ of the following with suitable reasons:
A circle has only finite number of equal chords.
View full solution →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.
View full solution →Fill in the blanks: A circle divides the plane, on which it lies, in $...........$ parts.
View full solution →Fill in the blanks: An arc is a $...........$ when its ends are the ends of a diameter.
View full solution →Fill in the blanks: A point whose distance from the center of a circle is greater than its radius lies in $...........$ of the circle.
View full solution →Fill in the blanks: A continuous piece of a circle is $...........$ of the circle.
View full solution →Fill in the blanks: The longest chord of a circle is a $...........$ of the circle.
View full solution →
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:
View full solution →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:
View full solution →If $O$ is the centre of the circle, find the value of $x$ in the following figure:
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 $\angle\text{CAO.}$ 
View full solution →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 $5\ cm, 11\ cm$ respectively of a circle are parallel. If the distance between $AB$ and $CD$ is $3\ cm$, find the radius of the circle.
View full solution →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 $\angle\text{OAC.}$
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