In the given figure, O is the centre of a circle. Then, $\angle\text{OAB}=?$
- A50°
- B60°
- C55°
- D65°
Question types
Circles question types
408 questions across 9 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
408
Questions
9
Question groups
5
Question types
01
M.C.Q
244 Q→02Fill In The Blanks[1 Marks ]
8 Q→03True False[1 Marks ]
18 Q→041 Marks Question
3 Q→05Match the Following.
2 Q→062 Marks Questions
8 Q→073 Marks Question
10 Q→084 Marks Questions
107 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.
In the given figure, O is the centre of a circle and $\angle\text{AOB}=140^\circ.$ Then, $\angle\text{ACB}=?$
- A70°
- B80°
- C110°
- D40°
- A130º
- B100º
- C80º
- D90º
The greatest chord of a circle is called its:
- ARadius.
- BSecant.
- CDiameter.
- DNone of these.
- A50º
- B40º
- C25º
- D75º
The longest chord of a circle is a _________ of the circle. (Radius, Diameter, Arc)
A segment of a circle is a region between an arc and _________ of the circle. (Chord, Center, Radius)
Circles having the same centre and different radii are called ___________ circles. (Concentric, Tangent, Secant)
A point whose distance from the center of a circle is greater than its radius lies in the _________ of the circle. (Interior, Exterior, Circumference)
An arc is a _______ when its ends are the ends of a diameter. (Sector, Semi-circle, Segment)
If A, B, C and D are four points such that $\angle\text{BAC}=45^\circ$ and $\angle\text{BDC}=45^\circ,$ then A, B, C, D are concyclic.
View full solution →The degree measure of an arc is the complement of the central angle containing the arc.
A chord of a circle, which is twice as long is its radius is a diameter of the circle.
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 →Two chords AB and CD of a circle are each at distances 4cm from the centre. Then AB = CD.
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.
View full solution →In the given figure, two circles intersect at two points A and B. AD and AC are diameters to the circles. Prove that B lies on the line segment DC.
| Column 1 | Column 2 | ||
| Q.1. | The total length of a circle is called the __________ of the circle. | A. | Diameter |
| Q.2. | The longest chord of a circle is the __________ of the circle. | B. | Circumference |
| C. | Arc |
| Column 1 | Column 2 | ||
| Q.1. | In a cyclic quadrilateral PQRS ,if 5$\angle Q $ =7$\angle S $ , then $\angle Q $ =__________ | A. | 90° |
| Q.2. | If XY is the diameter of the circumcircle of $\triangle X Y Z$ , then $\angle X Z Y$ =__________ | B. | 150° |
| C. | 100° |
In given figure, $\angle$ABC = 69°, $\angle$ACB = 31°, 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, A, B, C are three points on a circle with centre O such that $\angle$BOC = 30°, $\angle$AOB = 60°. If D is a point on the circle other than the arc 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.
ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If $\angle$ DBC = 70o, $\angle$BAC is 30o, 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.
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?
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.
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