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Circle MATHS - Circle

Rajasthan Board (RBSE) - STD 9 - MATHS (Rajasthan - English Medium). 109 questions in this chapter.

Question types

Circle question types

109 questions across 4 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.

109
Questions
4
Question groups
5
Question types
Sample Questions

Circle questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q1 Mark
In the given figure$, CD$ is the diameter of a circle with centre $O$ and $CD$ is perpendicular to chord $AB.$ If $AB = 12\ cm$ and $CE = 3\ cm,$ then radius of the circles is:
  • A
    $6\ cm$
  • B
    $9\ cm$
  • ✓
    $7.5\ cm$
  • D
    $8\ cm$

Answer: C.

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Q 2M.C.Q1 Mark
The radius of a circle is $13\ cm$ and the length of one of its chords is $10\ cm.$ The distance of the chord from the centre is:
  • A
    $11.5\text{ cm}$
  • ✓
    $12\text{ cm}$
  • C
    $\sqrt{69}\text{ cm}$
  • D
    $23\text{ cm}$

Answer: B.

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Q 3M.C.Q1 Mark
 In the given figure, BOC is a diameter of a circle with centre O. If $\angle\text{BCA}=30^\circ$ then $\angle\text{CDA}=?$
  1. 30°
  2. 45°
  3. 60°
  4. 50°
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Q 4M.C.Q1 Mark
In the given figure ABCD is a cyclic quadrilateral in which AB || DC and $\angle\text{BAD}=100^\circ.$ Then, $\angle\text{ABC}=?$
  1. 80°
  2. 100°
  3. 50°
  4. 40°
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Q 5M.C.Q1 Mark
In the given figure, O is the centre of a circle and chords AC and BD intersect at E. If $\angle\text{AEB}=110^\circ$ and $\angle\text{CBE}=30^\circ,$ then $\angle\text{ADB}=?$
  1. 70°
  2. 60°
  3. 80°
  4. 90°
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Q 63 Marks Question3 Marks
In the given figure, ABCD is a cyclic quadrilateral whose diagonals intersect at P such that $\angle\text{DBC}=60^\circ$and $\angle\text{BAC}=40^\circ.$ Find 
  1. $\angle\text{BCD}$
  2. $\angle\text{CAD}$
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Q 83 Marks Question3 Marks
In the given figure, O is the canter of the circle and $\angle\text{AOB}=70^\circ.$ Calculate the values of
  1. $\angle\text{OCA}$
  2. $\angle\text{OAC}$
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Q 93 Marks Question3 Marks
In the given figure, AB is a chord of a circle with centre O and AB is produced to C such that BC = OB. Also, CO is joined and produced to meet the circle in D. If $\angle\text{ACD}=\text{y}^\circ$ and $\angle\text{AOD}=\text{x}^\circ,$ prove that x = 3y.
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Q 103 Marks Question3 Marks
In the given figure $\triangle\text{ABC}$ is an isosceles triangle in which AB = AC and a circle passing through B andC intersects AB and AC at D and E respectively. Prove that DE || BC.
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Q 115 Marks Questions5 Marks
  1. In Figure (1), O is the centre of the circle. If $\angle\text{OAB}=40^\circ$ and $\angle\text{OCB}=30^\circ,$ find $\angle\text{AOC}.$
  2.  In Figure (2), A, B and C are three points on the circle with centre O such that $\angle\text{AOB}=90^\circ$ and $\angle\text{AOC}=110^\circ.$ Find $\angle\text{BAC}.$

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Q 125 Marks Questions5 Marks
Two circles with centres O and O' intersect at two points A and B. A line PQ is drawn parallel to OO' through A or B, intersecting the circles at P and Q. Prove that PQ = 2OO'.
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Q 135 Marks Questions5 Marks
In the given figure, ABCD is a cyclic quadrilateral in which AE is drawn parallel to CD, and BA is produced. If $\angle\text{ABC}=92^\circ$ and $\angle\text{FAE}=20^\circ,$ find $\angle\text{BCD}.$
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Q 155 Marks Questions5 Marks
In the adjoining figure, ABCD is a cyclic quadrilateral in which $\angle\text{BCD}=100^\circ$ and $\angle\text{ABD}=50^\circ.$ Find $\angle\text{ADB}.$
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Q 174 Marks Questions4 Marks
In the given figure, O is the centre of the circle. if $\angle\text{PBC}=25^\circ$ and $\angle\text{APB}=110^\circ,$find the value of $\angle\text{ADB}.$
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Q 204 Marks Questions4 Marks
In the given figure, $\angle\text{BAD}=75^\circ,\angle\text{DCF}=\text{x}^\circ$ and $\angle\text{DEF}=\text{y}^\circ.$ Find the values of x and y.
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