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Circles Maths - Circles

Gujarat Board (GSEB) - STD 10 - Maths (GSEB - English Medium). 125 questions in this chapter.

Question types

Circles question types

125 questions across 5 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

125
Questions
5
Question groups
5
Question types
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.

Q 1M.C.Q (1 Marks)1 Mark
In the given figure, $QR$ is a common tangent to the given circles touching externally at the point $T$. The tangent at $T$ meets $QR$ at $P$. If $PT = 3.8cm$, then the length of
$QR$ (in cm) is:
  • A
    $3.8$
  • ✓
    $7.6$
  • C
    $5.7$
  • D
    $1.9$

Answer: B.

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Q 2M.C.Q (1 Marks)1 Mark
In the figure, a quadrilateral $ABCD$ is drawn to circumscribe a circle such that its sides $AB, BC, CD$ and $AD$ touch the circle at $P, Q, R$ and $S$ respectively.
If $AB = x\ cm$$, BC= 7\ cm, CR = 3\ cm$ and $AS = 5\ cm$, then $x =$
  • A
    $10$
  • ✓
    $9$
  • C
    $8$
  • D
    $7$

Answer: B.

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Q 3M.C.Q (1 Marks)1 Mark
In the given figure, if $AD, AE$ and $BC$ are tangents to the circle at $D, E$ and $F$ respectively, Then:
  • A
    $AD = AB + BC + CA$
  • ✓
    $2AD = AB + BC + CA$
  • C
    $3AD = AB + BC + CA$
  • D
    $4AD = AB + BC + CA$

Answer: B.

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Q 4M.C.Q (1 Marks)1 Mark
The length of the tangent from a point $A$ at a circle, of radius $3\ cm,$ is $4\ cm$. The distance of $A$ from the centre of the circle is:
  • A
    $\sqrt{7}\text{cm}$
     
  • B
    $7\ cm$
     
  • ✓
    $5\ cm$
     
  • D
    $25\ cm$

Answer: C.

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Q 5M.C.Q (1 Marks)1 Mark
If $PT$ is tahgent drawn froth a point P to a circle touching it at $T$ and $O$ is the centre of the circle, then $∠OPT + ∠POT =$
  • A
    $30^\circ$
  • B
    $60^\circ$
  • ✓
    $90^\circ$
  • D
    $180^\circ$

Answer: C.

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Q 122 Marks Questions2 Marks
In the figure, $BOA$ is a diameter of a circle and the tangent at a point $P$ meets $BA$ produced at $T.$ If $\angle\text{PBO}=30^{\circ}$ then find $\angle\text{PTA}.$
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Q 132 Marks Questions2 Marks
In the figure, $PQL$ and $PRM$ are tangents to the circle with centre $O$ at the points $Q$ and $R$ respectively and $S$ is a point on the circle such that $\angle\text{SQL}=50^{\circ}$ and
$\angle\text{SRM}=60^{\circ}.$ Then, find $\angle\text{QSR}.$
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Q 142 Marks Questions2 Marks
In the figure, $CP$ and $CQ$ are tangents from an external point $C$ to a circle with centre $O. AB$ is another tangent which touches the circle at $R.$ If $CP = 11\ cm$ and $BR = 4\ cm,$ find the length of $BC.$
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Q 152 Marks Questions2 Marks
In the figure, $PA$ and $PB$ are tangents to the circle drawn from an external point $P.\ CD$ is a third tangent touching the circle at $Q$. If $PB = 10\ cm$ and $CQ = 2\ cm,$ what is
the length $PC?$
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Q 163 Marks Question3 Marks
In the given figure, there are two concentric circles with centre $O$ of radii 5cm and 3cm. From an external point $P,$ tangent $PA$ and $PB$ are drawn to these circles.
If $AP = 12\ cm,$ find the length of $BP.$
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Q 183 Marks Question3 Marks
If $PA$ and $PB$ are tangents from an outside point $P$ such that $PA = 10\ cm$ and $\angle\text{APB}=60^{\circ}.$ Find the length of chord $AB.$
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Q 193 Marks Question3 Marks
$A$ is a point at a distance $13\ cm$ from the centre $O$ of a circle of radius $5\ cm. AP$ 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 $\triangle\text{ABC}.$
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Q 203 Marks Question3 Marks
In the figure, $PQ$ is a chord of a circle and $PT$ is the tangent at $P$ such that $\angle\text{QPT}=60^{\circ}.$ Then, find $\angle\text{PRQ}$.
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Q 214 Marks Questions4 Marks
$AB$ 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 $AB$ at a point $D$. Prove that $BC = BD.$
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Q 234 Marks Questions4 Marks
In the given figure, $BDC$ is a tangent to the given circle at point $D$ such that $BD =30 cm$ and $CD =7 cm$. The other tangents $BE$ and $CF$ are drawn respectively
from $B$ and $C$ to the circle and meet when produced at A making $BAC$ a right angle triangle. Calculate $(i) AF (ii)$ radius of the circle.
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Q 244 Marks Questions4 Marks
In the given figure, $AB$ is a chord of length $16\ cm$ of a circle of radius $10\ cm$. The tangents at $A$ and $B$ intersect at a point $P$. Find the length of $PA.$
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Q 254 Marks Questions4 Marks
In the figure, $PQ$ is a tangent from an external point $P$ to a circle with centre $O$ and $OP$ cuts the circle at $T$ and $QOP$ is a diameter. If $\angle\text{POR}=130^{\circ}$ and $S$ is a point
on the circle, find $\angle1+\angle2.$
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