In the given figure, CD is the diameter of a circle with centre O and CD is perpendicular to chord AB. If AB = 12cm and CE = 3cm, then radius of the circles is:
- 6cm
- 9cm
- 7.5cm
- 8cm
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.
View full solution →
The radius of a circle is 13cm and the length of one of its chords is 10cm. The distance of the chord from the centre is:
View full solution →- $11.5\text{cm}$
- $12\text{cm}$
- $\sqrt{69}\text{cm}$
- $23\text{cm}$
In the given figure, BOC is a diameter of a circle with centre O. If $\angle\text{BCA}=30^\circ$ then $\angle\text{CDA}=?$
View full solution →- 30°
- 45°
- 60°
- 50°
In the given figure, O is the centre of a circle in which $\angle\text{OAB}=20^\circ$ and $\angle\text{OCB}=50^\circ.$ Then, $\angle\text{AOC}=?$
View full solution →- 50°
- 70°
- 20°
- 60°
In the given figure, O is the centre of a circle and $\angle\text{ACB}=30^\circ.$ Then, $\angle\text{AOB}=?$
View full solution →- 30°
- 15°
- 60°
- 90°
ABCD is a rectangle. Prove that the centre of the circle through A, B, C, D is the point of intersection of its diagonals.
In the given figure, O is the canter of the circle and $\angle\text{AOB}=70^\circ.$ Calculate the values of
View full solution →- $\angle\text{OCA}$
- $\angle\text{OAC}$
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.
View full solution →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.
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 diameter of a circle bisects each of the two chords of a circle then prove that the chords are parallel.
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 $\angle\text{ADB}.$
View full solution →Prove that the perpendicular bisectors of the sides of a cyclic quadrilateral are concurrent.
Prove that the circles described with the four sides of a rhombus, as diameters, pass through the point of intersection of its diagonals.
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.
View full solution →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'.
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 $\angle\text{BCD}.$
View full solution →Two equal circles intersect in P and Q. A straight line through P meets the circles in A and B. Prove that QA = QB.
In the adjoining figure, ABCD is a cyclic quadrilateral in which $\angle\text{BCD}=100^\circ$ and $\angle\text{ABD}=50^\circ.$ Find $\angle\text{ADB}.$
View full solution →In the given figure, POQ is a diameter and PQRS is a cyclic quadrilateral. If $\angle\text{PSR}=150^\circ,$ find $\angle\text{RPQ}.$
View full solution →Generate a Circle paper free
Pick question groups from the list above, set marks and difficulty, and export a branded PDF with step-by-step answer keys. First 3 chapters free — no signup.