In Figure, if O is the centre of a circle, PQ is a chord and the tangent PR at P makes an angle of 50° with PQ, then $\angle\text{POQ}$ is equal to:
- ✓100°
- B80°
- C90°
- D75°
Answer: A.
View full solution →Question types
Circles question types
42 questions across 5 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
42
Questions
5
Question groups
5
Question types
01
M.C.Q (1 Marks)
8 Q→02True False[1 Marks ]
10 Q→032 Marks Questions
1 Q→043 Marks Question
5 Q→055 Marks Questions
18 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 figure, if $\angle\text{AOB}=125^\circ,$ then $\angle\text{COD}$ is equal to:
- A62.5°
- B45°
- C35°
- ✓55°
Answer: D.
View full solution →If two tangents inclined at an angle 60° are drawn to a circle of radius 3cm, then length of each tangent is equal to:
- A$\frac{3}{2}\sqrt{3}\text{cm}$
- B$6\text{cm}$
- C$3\text{cm}$
- ✓$3\sqrt{3}\text{cm}$
Answer: D.
View full solution →In figure, AB is a chord of the circle and AOC is its diameter such that $\angle\text{ACB}=50^\circ.$ If AT is the tangent to the circle at the point A, then $\angle\text{BAT}$ is equal to:
- A65°
- B60°
- ✓50°
- D40°
Answer: C.
View full solution →In Figure, if PQR is the tangent to a circle at Q whose centre is O, AB is a chord parallel to PR and $\angle\text{BQR}=70^\circ,$ then $\angle\text{AQB}$ is equal to:
- A20°
- ✓40°
- C35°
- D45°
Answer: B.
View full solution →Write ‘True’ or ‘False’ and justify your answer.
The angle between two tangents to a circle may be 0°.
The angle between two tangents to a circle may be 0°.
Write ‘True’ or ‘False’ and justify your answer.
If angle between two tangents drawn from a point P to a circle of radius a and centre O is 90°, then $\text{OP}=\text{a}\sqrt{2}.$
View full solution →If angle between two tangents drawn from a point P to a circle of radius a and centre O is 90°, then $\text{OP}=\text{a}\sqrt{2}.$
Write ‘True’ or ‘False’ and justify your answer.
The length of tangent from an external point P on a circle with centre O is always less than OP.
The length of tangent from an external point P on a circle with centre O is always less than OP.
Write ‘True’ or ‘False’ and justify your answer.
The tangent to the circumcircle of an isosceles triangle$\triangle\text{ABC}$ at A, in which AB = AC, is parallel to BC.
View full solution →The tangent to the circumcircle of an isosceles triangle$\triangle\text{ABC}$ at A, in which AB = AC, is parallel to BC.
Write ‘True’ or ‘False’ and justify your answer.
AB is a diameter of a circle and AC is its chord such that $\angle\text{BAC}=30^\circ.$ If the tangent at C intersects AB extended at D, then BC = BD.
View full solution →AB is a diameter of a circle and AC is its chord such that $\angle\text{BAC}=30^\circ.$ If the tangent at C intersects AB extended at D, then BC = BD.
Two tangents PQ and PR are drawn from an external point to a circle with centre O. Prove that QORP is a cyclic quadrilateral.
Out of the two concentric circles, the radius of the outer circle is 5cm and the chord $AC$ of length 8cm is a tangent to the inner circle. Find the radius of the inner circle.
View full solution →If from an external point B of a circle with centre O, two tangents BC and BD are drawn such that $\angle\text{DBC}=120^\circ,$ prove that BC + BD = BO, i.e., BO = 2BC.
View full solution →Prove that a diameter AB of a circle bisects all those chords which are parallel to the tangent at the point A.
A chord PQ of a circle is parallel to the tangent drawn at a point R of the circle. Prove that R bisects the arc PRQ.
In Figure, common tangents AB and CD to two circles intersect at E. Prove that AB = CD.
A is a point at a distance 13cm from the centre O of a circle of radius 5cm. AP and AQ are the tangents to the circle at P and Q. If a tangent BC is drawn at a point R lying on the minor arc PQ to intersect AP at B and AQ at C, find the perimeter of the $\triangle\text{ABC}.$
View full solution →AB is a diameter and AC is a chord of a circle with centre O such that $\angle\text{BAC}=30^\circ.$ The tangent at C intersects extended AB at a point D. Prove that BC = BD.
View full solution →Prove that the centre of a circle touching two intersecting lines lies on the angle bisector of the lines.
In Figure, AB and CD are common tangents to two circles of unequal radii. Prove that AB = CD.
In Figure, the common tangent, AB and CD to two circles with centres O and O' intersect at E. Prove that the points O, E, O' are collinear.
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