A chord of a circle of radius $10 \ cm$ subtends a right angle at its centre. The length of the chord $($in $cm )$ is
- ✓$5 \sqrt{2}$
- B$10 \sqrt{2}$
- C$\frac{5}{\sqrt{2}}$
- D$10 \sqrt{3}$
Answer: A.
View full solution →Question types
Circles question types
70 questions across 5 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
70
Questions
5
Question groups
5
Question types
01
M.C.Q (1 Marks)
37 Q→021 Marks Question
6 Q→032 Marks Questions
18 Q→043 Marks Question
7 Q→055 Marks Questions
2 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, $P Q$ and $P R$ are two tangents to a circle with centre $O$. If $\angle P Q R=46^{\circ},$ then $\angle Q O R$ equals:
- A$67^{\circ}$
- ✓$134^{\circ}$
- C$44^{\circ}$
- D$46^{\circ}$
Answer: B.
View full solution →In a right triangle $\text{ABC}$, right $-$ angled at $B, BC =12 \ cm$ and $AB =5 \ cm$. The radius of the circle inscribed in the triangle $($in $\ cm )$ is
- A$4$
- B$3$
- ✓$2$
- D$1$
Answer: C.
View full solution →Two circles touch each other externally at $\text{P.AB}$ is a common tangent to the circles touching them at $A$ and $B$. The value of $\angle \text{APB}$ is
- ✓$30^{\circ}$
- B$45^{\circ}$
- C$60^{\circ}$
- D$90^{\circ}$
Answer: A.
View full solution →In figure, $\text{QR}$ is a common tangent to the given circles, touching externally at the point $T$. The tangent at $T$ meets $\text{QR}$ at $P$. If $\text{QP} =3.8$, then the length of $\text{QR} ($in $cm )$ is :
- A$3.8$
- ✓$7.6$
- C$5.7$
- D$1.9$
Answer: B.
View full solution →From an external point $P$, tangents $P A$ and $P B$ are drawn to a circle with centre $O$. If $\angle P A B=50^{\circ},$ then find $\angle A O B$.
View full solution →If the angle between two tangents drawn from an external point $P$ to a circle of radius a and centre $O,$ is $60^{\circ},$ then find the length of $O P$.
View full solution →In Fig. $, AB$ is the diameter of a circle with centre $O$ and $A T$ is a tangent. If $\angle A O Q=58^{\circ},$ find $\angle A T Q$.
View full solution →In given Fig., $P A$ and $P B$ are tangents to the circle with centre 0 such that $\angle A P B=50^{\circ}$. Write the measure of $\angle O A B$.
View full solution →In given Figure, the length $PB =$ _____________ cm .
View full solution →In the given figure, $P A$ and $P B$ are tangents to the circle from an external point $P . C D$ is another tangent touching the circle at $Q$. If $P A=12 cm$, $Q C=Q D=3 cm$, then find $P C+P D$.
View full solution →Prove that the tangents drawn at the end points of a chord of a circle make equal angles with the chord.
In Fig., $A P$ and $B P$ are tangents to a circle with centre $O$, such that $A P=5 \ cm$ and $\angle A P B=60^{\circ}$. Find the length of chord $A B$
View full solution →In the given figure, from an external point $P,$ two tangents $P T$ and $P S$ are drawn to a circle with centre $O$ and radius $r$. If $O P=2 r,$ show that $\angle O T S=\angle O S T=30^{\circ}$
View full solution →If from an external point $P$ of a circle with center $O$, two tangents $P Q$ and $P R$ are drawn such that $\angle Q P R=120^{\circ}$, prove that $2 P Q=P O$
View full solution →Two tangents $T P$ and $T Q$ are drawn to a circle with centre $O$ from an external point $T$. Prove that $\angle P T Q=2 \angle O P Q$.
View full solution →In figure, two tangents $R Q$ and $R P$ are drawn from an external point $R$ to the circle with centre $O$. If $\angle P R Q=120^{\circ}$, then prove that $O R=P R+R Q$.
View full solution →From a point $T$ outside a circle of centre $O$, tangents $T P$ and TQ are drawn to the circle. Prove that $O T$ is the right bisector of line segment $P Q$.
View full solution →In Figure, a circle is inscribed in a triangle $P Q R$ with $PQ =10 \ cm, Q R=8 \ cm$ and $P R=12 \ cm$. Find the lengths $Q M, R N$ and $P L$.
View full solution →In the given figure, a triangle $\text{ABC}$ is drawn to circumscribe a circle of radius $2 \ cm$ such that the segments $B D$ and $D C$ into which $B C$ is divided by the point of contact $D$ are of lengths $4 \ cm$ and $3 \ cm$ respectively. If area of $\triangle A B C=21 \ cm^2,$ then find the lengths of sides $A B$ and $A C$.
View full solution →A circle touches the side $B C$ of a $\triangle A B C$ at a point $P$ and touches $A B$ and $A C$ when produced at $Q$ and $R$ respectively. Show that $AQ =\frac{1}{2} ($Perimeter of $\triangle A B C ).$
View full solution →Two tangents $TP$ and $TQ$ are drawn to a circle with centre $O$ from an external point $T$. Prove that $\angle PIQ =2 \angle OPQ$.
View full solution →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.