In the given figure, $RQ$ is a tangent to the circle with centre $O$. If $SQ = 6cm$ and $QR = 4cm,$ then $OR $is equal to:
- A$2.5cm$
- B$3cm$
- ✓$5cm$
- D$8cm$
Answer: C.
View full solution →Question types
Circles question types
98 questions across 5 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
98
Questions
5
Question groups
5
Question types
01
M.C.Q (1 Marks)
56 Q→02Assertion (A) & Reason (B) MCQ
3 Q→032 Marks Questions
12 Q→043 Marks Question
12 Q→054 Marks Questions
15 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, $QR$ is a common tangent to the given circle, touching externally at the point $T$. The tangent at $T$ meets $QR$ at $P$. If $PT = 3.8cm$ then the length of $QR$ is:
- A$1.9cm$
- B$3.8cm$
- C$5.7cm$
- ✓$7.6cm$
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 $ABCD$ is circumscribed, touching the circle at $P, Q, R $and S. If $AP = 5cm$, $BC = 7cm$ and $CS = 3cm, AB =?$
- ✓$9cm$
- B$10cm$
- C$12cm$
- D$8cm$
Answer: A.
View full solution →In the given figure, $O$ is the centre of two concentric circles of radii $5cm$ and $3cm$. From an external point $P$ tangents $PA$ and $PB$ are drawn to these circles. If PA = $12cm$ then $PB$ is equal to:
- A$5\sqrt{2}\text{cm}$
- B$3\sqrt{5}\text{cm}$
- ✓$4\sqrt{10}\text{cm}$
- D$5\sqrt{10}\text{cm}$
Answer: C.
View full solution →Assertion $(A) :$ In the given figure, $a$ quad. $ABCD$ is drawn to circumscribe a given circle as shown.
Reason $(R) :$ In two concentric circles, the chord of the larger circle, which to uches the smaller circle, is bisected at the point of contact.
Reason $(R) :$ In two concentric circles, the chord of the larger circle, which to uches the smaller circle, is bisected at the point of contact.
- ABoth 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.
- ✓Assertion $(A)$ is false and Reason $(R)$is true.
Answer: D.
View full solution →Assertion $(A)$ : If two tangent are drawn to a circle from an external point then they subtend equal angles at the centre.
Reason $(R)$ : A parallelogram circumscribing a circle is a rhombus.
Reason $(R)$ : A parallelogram circumscribing a circle is a rhombus.
- ABoth Assertion $(A)$ and Reason $(R)$ are true and Reason $(R)$ is a correct explanation of Assertion $(A)$.
- ✓Both 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: B.
View full solution →Assertion (A) : At a point P of a circle with centre O and radius 12cm, a tangent PQ of length 16cm is drawn. Then, the point of contact. OQ = 20cm.
Reason (R) : The tangent at any point of a circle is perpendicular to the radius through the point of contact.
Reason (R) : The tangent at any point of a circle is perpendicular to the radius through the point of contact.
- ✓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 →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 $AB = 12cm, BC = 8\ cm$ and $AC = 10\ cm$, find the lengths of $AD, BE$ and $CF$.
View full solution →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.
View full solution →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 $AC = CB$.
View full solution →In the given figure, an isosceles triangle $ABC$, with $AB = AC$, circumscribes a circle. Prove that the point of contact $P$ bisects the base $BC$.
View full solution →In the adjoining figure, a circle touches all the four sides of a quadrilateral $ABCD$ whose sides are $AB = 6\ cm, BC = 9\ cm$ and $CD = 8\ cm.$ Find the length of $AD.$
View full solution →A point $P$ is $25\ cm$ away from the centre of a circle and the length of tangent drawn from $P$ to the circle is $24\ cm$. Find the radius of the circle.
View full solution →In the given figure, a circle touches all the four sides of a quadrilateral $ABCD$ whose three sides are $AB = 6\ cm, BC = 7\ cm$ and $CD = 4\ cm.$ Find $AD.$
View full solution →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 $P A$ and $P B$ are drawn to a circle with centre $O$. If $C D$ is the tangent to the circle at a point $E$ and $P A=14 cm$, find the perimeter of $\triangle P C D$.
View full solution →$PQ$ is a chord of length $16\ cm$ of a circle of radius $10\ cm$. 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 $TP.$
Generate a Circles 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.