In the given figure, $RQ$ is a tangent to the circle with centre $O$. If $SQ = 6\ cm$ and $QR = 4\ cm$, then $OR$ is equal to:
- A$2.5\ cm$
- B$3\ cm$
- ✓$5\ cm$
- D$8\ cm$
Answer: C.
View full solution →Question types
Circles question types
121 questions across 6 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
121
Questions
6
Question groups
5
Question types
01
M.C.Q (1 Marks)
59 Q→022 Marks Questions
24 Q→033 Marks Question
12 Q→044 Marks Questions
13 Q→055 Marks Question
2 Q→06Fill in the Blanks
11 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.
Each question consists of two statements, namely, Assertion $(A)$ and Reason $(R)$. for selecting the correct answer, use the following code:
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Assertion $(A)$
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Reason $(R)$
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At a point $P$ of a circle with centre $O$ and radius $12cm$, a tangent $PQ$ of length $16\ cm$ is drawn. Then, the point of contact. $OQ = 20\ cm.$
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The tangent at any point of a circle is perpendicular to the radius through the point of contact.
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- ✓Both Assertion $(A)$ and Reason $(R)$ are true and Reason $(R)$ is a correct explanation of Assertion $(A).$
- BBoth Assertion $(A)$ and Reason $(R)$ are true but Reason $(R)$ is not a correct explanation of Assertion $(A).$
- CAssertion $(A)$ is true and Reason $(R)$ is false.
- DAssertion $(A)$ is false and Reason $(R)$ is true.
Answer: A.
View full solution →In the given figure, $QR$ is a common tangent to the given circle, touching externally at the point $T$. The tangent at $T$ meets $QR$ at $P$. If $PT = 3.8\ cm$ then the length of $QR$ is:
- A$1.9\ cm$
- B$3.8\ cm$
- C$5.7\ cm$
- ✓$7.6\ cm$
Answer: D.
View full solution →In the given figure, $AB$ and $AC$ are tangent to the circle with centre $O$ such that $\angle\text{BAC}=40^\circ.$ Then, $\angle\text{BOC}$ is equal to:
- A$80^\circ$
- B$100^\circ$
- C$120^\circ$
- ✓$140^\circ$
Answer: D.
View full solution →In the given figure, quadrilateral $\text{ABCD}$ is circumscribed, touching the circle at $P, Q, R$ and $S.$ If $AP = 5\ cm, BC = 7\ cm$ and $CS = 3\ cm, AB =?$
- ✓$9cm$
- B$10cm$
- C$12cm$
- D$8cm$
Answer: A.
View full solution →Two tangents BC and BD are drawn to a circle with centre O, such that $\angle\text{CBD} = 120^\circ.$ Prove that OB= 2BC.
View full solution →In the given figure, a circle inscribed in a triangle ABC, touches the sides AB, BC and AC at points D, E and F respectively. If AB = 12cm, BC = 8cm and AC = 10cm, find the lengths of AD, BE and CF.
In the given figure, PA and PB are the tangents to a circle with centre O. Show that the points A, O, B, P are concyclic.
In the given figure, the chord AB of the larger of the two concentric circles, with centre O, touches the smaller circle at C. Prove that AC = CB.
In the given figure, an isosceles triangle ABC, with AB = AC, circumscribes a circle. Prove that the point of contact P bisects the base BC.
In the adjoining figure, a circle touches all the four sides of a quadrilateral ABCD whose sides are AB = 6cm, BC = 9cm and CD = 8cm. Find the length of AD.
A point P is 25cm away from the centre of a circle and the length of tangent drawn from P to the circle is 24cm. Find the radius of the circle.
In the given figure, a circle touches all the four sides of a quadrilateral ABCD whose three sides are AB = 6cm, BC = 7cm and CD = 4cm. Find AD. 
In the given figure, O is the centre of the circle and TP is the tangent to the circle from an external point T. If $\angle\text{PBT} = 30^\circ,$prove that
BA : AT = 2 : 1.
View full solution →BA : AT = 2 : 1.
In the given figure, PQ is a chord of a circle with centre O and PT is a tangent. If $\angle\text{QPT} = 60^\circ ,$ find $\angle\text{PRQ}.$
View full solution →Prove that the perpendicular at the point of contact of the tangent to a circle passes through the centre.
A quadrilateral is drawn to circumscribe a circle. Prove that the sume of opposite sides are equal.
In the given figure, O is the centre of a circle PT and PQ are tangents to the circle from an external point P. If $\text{TPQ} = 70^\circ$ then$ \angle\text{TRQ} .$
View full solution →From an external point P, tangents PA and PB are drawn to a circle with centre O. If CD is the tangent to the circle at a point E and PA = 14cm, find the perimeter of $\triangle\text{PCD}.$
View full solution →$PQ$ is a chord of length $16cm$ of a circle of radius 10cm. The tangent at $ P$ and $Q$ intersect at point T as shown in the figure.
Finf the length of $TP.$
View full solution →Finf the length of $TP.$
Prove that the opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.
Prove that the angle between the two tangent drawn from an external point to a circle is supplenentary to the angle subtended by the line segments joining the points of contact at the centre.
Prove that the lengths drawn at the diameter of a circle are parallel.
Two concentric circle are of radii $5\ cm$ and $3\ cm$ respectively. Find the length of the chord of the larger circle which touches the smaller circle.
View full solution →Prove that the tangent drawn at the ends of a chord of a circle make equal angles with chord.
Fill in the blanks.
A line intersecting a circle in two distinct points is called a ___________.
A line intersecting a circle in two distinct points is called a ___________.
Prove that the lengths of two tangents drawn from an external point to a circle are equal.
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