Write the correct answer in the following: In Fig. if $OA = 5\ cm, AB = 8\ cm$ and $OD$ is perpendicular to $AB$, then $CD$ is equal to: 
- A$2\ cm$.
- B$3\ cm$.
- ✓$4\ cm$.
- D$5\ cm$.
Answer: C.
View full solution →Question types
Circles question types
54 questions across 6 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
54
Questions
6
Question groups
5
Question types
01
M.C.Q
10 Q→02True False[1 Marks ]
10 Q→032 Marks Questions
1 Q→043 Marks Question
4 Q→055 Marks Questions
1 Q→064 Marks Questions
28 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.
Write the correct answer in the following: In Fig. $BC$ is a diameter of the circle and $\angle\text{BAO}=60^\circ.$ Then $\angle\text{ADC}$ is equal to:
- A$30^\circ$.
- B$45^\circ$.
- ✓$60^\circ$.
- D$120^\circ$.
Answer: C.
View full solution →Write the correct answer in the following: In Fig. $\angle\text{AOB}=90^\circ$ and $\angle\text{ABC}=30^\circ,$ then $\angle\text{CAO}$ is equal to:
- A$30^\circ .$
- B$45^\circ .$
- C$90^\circ .$
- ✓$60^\circ .$
Answer: D.
View full solution →Write the correct answer in the following: In Fig. if $\angle\text{OAB}=40^\circ,$ then $\angle\text{ACB}$ is equal to: 
- ✓$50^\circ .$
- B$40^\circ .$
- C$60^\circ .$
- D$70^\circ .$
Answer: A.
View full solution →Write the correct answer in the following:
In Fig. if $\angle\text{DAB} = 60^\circ, \angle\text{ABD} = 50^\circ,$ then $\angle\text{ACB}$ is equal to:
In Fig. if $\angle\text{DAB} = 60^\circ, \angle\text{ABD} = 50^\circ,$ then $\angle\text{ACB}$ is equal to:
- A$60^\circ .$
- B$50^\circ .$
- ✓$70^\circ .$
- D$80^\circ .$
Answer: C.
View full solution →Write True or False and justify your answer in the following: $ABCD$ 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 →Write True or False and justify your answer in the following: If $AOB$ is a diameter of a circle and $C$ is a point on the circle, then $AC ^2+B C^2=A B^2$
View full solution →Write True or False and justify your answer in the following: Two congruent circles with centres $O$ and $O′$ intersect at two points $A$ and $B.$ Then $\angle\text{AOB}=\angle\text{AO'B}.$
View full solution →Write True or False and justify your answer in the following: Two chords $AB$ and $AC$ of a circle with centre $O$ are on the opposite sides of $OA.$ Then $\angle\text{OAB}=\angle\text{OAC}.$
View full solution →Write True or False and justify your answer in the following: $A$ circle of radius $3\ cm$ can be drawn through two points $A, B$ such that $AB = 6\ cm.$
View full solution →If arcs $AXB$ and $CYD$ of a circle are congruent, find the ratio of $AB$ and $CD.$
View full solution →In Fig. $AOB$ is a diameter of the circle and $C, D, E$ are any three points on the semi-circle. Find the value of $\angle\text{ACD} + \angle\text{BED.}$
View full solution →If the perpendicular bisector of a chord $AB$ of a circle $PXAQBY$ intersects the circle at $P$ and $Q$, prove that arc $\text{PXA}\cong\text{Arc PYB}.$
View full solution →Two chords $AB$ and $AC$ of a circle subtends angles equal to $90^\circ $ and $150^\circ $, respectively at the centre. Find $\angle\text{BAC},$ if $AB$ and $AC$ lie on the opposite sides of the centre.
View full solution →If BM and $CN$ are the perpendiculars drawn on the sides $AC$ and $AB$ of the triangle $ABC$, prove that the points $B, C, M $ and $N$ are concyclic.
View full solution →In Fig. $\angle\text{OAB} = 30^\circ$ and $\angle\text{OCB} = 57^\circ.$ Find $\angle\text{BOC}$ and $\angle\text{AOC}.$ 
View full solution →A quadrilateral $ABCD$ is inscribed in a circle such that $AB$ is a diameter and $\angle\text{ADC}=130^\circ.$ Find $\angle\text{BAC}.$
View full solution →$AB$ and $AC$ are two equal chords of a circle. Prove that the bisector of the angle $BAC$ passes through the centre of the circle.
View full solution →$ABCD$ is a parallelogram. $A$ circle through $A, B$ is so drawn that it intersects $AD$ at $P$ and $BC$ at $Q.$ Prove that $P, Q, C$ and $D$ are concyclic.
View full solution →On a common hypotenuse $AB,$ two right triangles $ACB$ and $ADB$ are situated on opposite sides. Prove that $\angle\text{BAC} = \angle\text{BDC.}$
View full solution →If a line is drawn parallel to the base of an isosceles triangle to intersect its equal sides, prove that the quadrilateral so formed is cyclic.
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