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Circles Maths - Circles

Jharkhand Board (JAC) - STD 10 - Maths (Jharkhand - English Medium). 232 questions in this chapter.

Question types

Circles question types

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

232
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= 7cm, CR = 3cm and AS = 5cm, 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°
  • B
    60°
  • ✓
    90°
  • D
    180°

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 = 11cm and BR = 4cm, 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 = 10cm and CQ = 2cm, 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 $ 3\ cm$. 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 193 Marks Question3 Marks
$A$ is a point at a distance $13 \ cm$ from the centre $O$ of a circle of radius $5 \ cm$ . $A P$ and $A Q$ are the tangents to the circle at $P$ and $Q$. If a tangent $B C$ is drawn at a point $R$ lying on the minor arc $P Q$ to intersect $A P$ at $B$ and $A Q$ at $C$, find the perimeter of the $\triangle A B C$.
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Q 215 Marks Questions5 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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