CIRCLES Test

CIRCLES

This is CIRCLES Test-01 for CBSE class 10 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
The length of tangent PQ, from an external point P is 24 cm. If the distance of the point P from the centre is 25 cm, then the diameter of the circle is
Question 1 figure 1
  • A
    14 cm.
    Correct
  • B
    15 cm.
  • C
    12 cm
  • D
    7 cm
2
A tangent PQ at a point P o a circle of radius 5 cm meets a line through the centre O at point Q, so that OQ = 12 cm. find the length PQ.
Question 2 figure 1
  • A
    \(\sqrt {113\;} cm\).
  • B
    \(\sqrt {119\;} cm\).
    Correct
  • C
    13 cm
  • D
    26 cm.
3
In the given figure, RQ is a tangent to the circle with centre O. If SQ = 6 cm and OR = 4 cm, then OR is equal to
Question 3 figure 1
  • A
    12 cm.
  • B
    5 cm.
    Correct
  • C
    2.5 cm.
  • D
    10 cm.
4
In the adjoining figure, the measure Of PR is
Question 4 figure 1
  • A
    12 cm.
  • B
    18 cm.
  • C
    16 cm.
    Correct
  • D
    10 cm.
5
In the figure given alongside the length of PR is
Question 5 figure 1
  • A
    20 cm.
  • B
    26 cm.
    Correct
  • C
    28 cm.
  • D
    24 cm.
6
If PT is a tangent to the circle with centre O, then x + y is equal to
Question 6 figure 1
  • A
    \(100^\circ \)
  • B
    \(75^\circ \)
  • C
    \(60^\circ \)
  • D
    \(90^\circ \)
    Correct
7
Of PT is a tangent of the circle with centre O and \(\angle TPO = 25^\circ \), then the measure of x is
Question 7 figure 1
  • A
    \(140^\circ \)
  • B
    \(150^\circ \)
  • C
    \(100^\circ \)
  • D
    \({115^ \circ }\)
    Correct
8
In the given figure, the measure of \(\angle {\text{OQP}}\)is
Question 8 figure 1
  • A
    \(35^\circ \)
  • B
    \(90^\circ \)
  • C
    \(60^\circ \)
  • D
    \({40^ \circ }\)
    Correct
9
AB is a chord of circle and AOC is its diameter such that \(\angle ACB = 40^\circ \). If AT is the tangent tot eh circle at the point A, then \(\angle BAT\) is equal to
Question 9 figure 1
  • A
    \(55^\circ \)
  • B
    \(60^\circ \)
  • C
    \(40^\circ \)
    Correct
  • D
    \(45^\circ \)
10
If O is the centre of a circle, PQ is a chord and tangent PR at P makes an angle of \(60^\circ \) with PQ, then\(\angle POQ\) is equal to
Question 10 figure 1
  • A
    \(110^\circ \)
  • B
    \(120^\circ \)
    Correct
  • C
    \(100^\circ \)
  • D
    \(90^\circ \)
11
Two concentric circles with centre O are of radii 6 cm and 3 cm. From an external point P, tangents PA and PBare drawn t these circles as shown in the figure. If AP = 10cm, then BP is equal to
Question 11 figure 1
  • A
    \(\sqrt {109} \) cm.
  • B
    \(\sqrt {91} \)
  • C
    \(\sqrt {127} \) cm.
    Correct
  • D
    \(\sqrt {119} \) cm.
12
AP is a tangent to the circle with centre O such that OP = 4 cm and \(\angle OPA = 30^\circ \). Then, AP is equal to
Question 12 figure 1
  • A
    \(3\sqrt 2 \) cm.
  • B
    2 cm.
  • C
    \(2\sqrt 3 \) cm.
    Correct
  • D
    \(2\sqrt 2 \)
13
In the given figure, O is the centre of the circle and PT is a tangent at T. If PC = 3 cm and PT = 6 cm, then the radius of the circle is equals to:
Question 13 figure 1
  • A
    5 cm
  • B
    6 cm
  • C
    7 cm
  • D
    4.5 cm
    Correct
14
If angle between two radii of a circle is \({130^o}\), the angle between tangents at ends of radii is :
  • A
    \(60^\circ \)
  • B
    \({50^ \circ }\)
    Correct
  • C
    \(70^\circ \)
  • D
    \(90^\circ \)
15
In figure, PT is tangent to the circle with centre O such that OP is 4 cm and \(\angle OPT = {30^o}\) length of tangent is given by :
Question 15 figure 1
  • A
    7 cm
  • B
    5 cm
  • C
    \(4\sqrt 3 \;cm\)
  • D
    \(2\sqrt 3 \;cm\)
    Correct