Maths MCQ Class X Ch-10 | Circle
Mathematics MCQ | Class 10 | Chapter 10
TANGENT TO A CIRCLE
Question 1.
A circle has a number of tangents equal to
(a) 0
(b) 1
(c) 2
(d) Infinite
Answer: (d) Infinite
Question 2.
In the given figure, point P is 26 cm away from the centre O of a circle and the length PT of the tangent drawn from P to the circle is 24 cm. Then the radius of the circle is
(a) 25 cm
(b) 26 cm
(c) 24 cm
(d) 10 cm
Ans: (d) 10 cm
3. A tangent intersects the circle at:
(a) One point
(b) Two distinct point
(c) At the circle
(d) None of the above
Answer: (a) One point
4. The distance between two parallel tangents of a circle is 18 cm, then the radius of the circle is
(a) 8 cm
(b) 10 cm
(c) 9 cm
(d) 7.5 cm
Answer: (c) 9 cm
5. A circle can have _____parallel tangents at a single time.
(a) One
(b) Two
(c) Three
(d) Four
Answer: (b) Two
6. In figure, AP, AQ and BC are tangents to the circle. If AB = 5 cm, AC = 6 cm and BC = 4 cm, then the length of AP (in cm) is
(a) 7.5
(b) 15
(c) 10
(d)
9
Ans: (a) 7.5
7. If the angle between two radii of a circle is 110º, then the angle between the tangents at the ends of the radii is:
(a) 90º
(b) 50º
(c) 70º
(c) 40º
Answer: (c) 70º
8. The angle in a semi-circle is _____
a) 90°
b) 180°
c) 0°
d) 360°
Answer (b)
9. The length of the tangent from an external point A on a circle with centre O is
(a) always greater than OA
(b) equal to OA
(c) always less than OA
(d) cannot be estimated
Answer: (c) always less than OA
10. What is the name of the point which is common to circle and the tangent?
a) Intersection point
b) Tangential point
c) Point of contact
d) Point of touch
Answer: (c)
11. AB is a chord of the circle and AOC is its diameter such that angle ACB = 50°. If AT is the tangent to the circle at the point A, then BAT is equal to
(a) 65°
(b) 60°
(c) 50°
(d)
40°
Answer: (c) 50°
12. Find the radius of a circle if 8 m is the length of the tangent, 11 m is the distance between the centre of the circle the external point.
a) 7 m
b) 5 m
c) √57 m
d) √58 m
Answer: (C)
13. If TP and TQ are the two tangents to a circle with centre O so that ∠POQ = 110°, then ∠PTQ is equal to
(a) 60°
(b) 70°
(c) 80°
(d)
90°
Answer: (b) 70°
14. Find the area of the circle if 8 cm is the length of the tangent, 11 cm is the distance between the centre of the circle the external point.
a) 100 cm
b) 110 cm
c) 197.14 cm
d) 179.14 cm
Answer: d
15. The length of a tangent from a point A at a distance 5 cm from the centre of the circle is 4 cm. The radius of the circle is:
(a) 3 cm
(b) 5 cm
(c) 7 cm
(d) 10 cm
Answer: (a) 3 cm
16. If a parallelogram circumscribes a circle, then it is a:
(a) Square
(b) Rectangle
(c) Rhombus
(d) None of the above
Answer: (c) Rhombus
Solution Hint: If a parallelogram circumscribes a circle, then it is
a Rhombus.
17. Two concentric circles are of radii 5 cm and 3 cm. The length of the chord of the larger circle which touches the smaller circle is:
(a) 8 cm
(b) 10 cm
(c) 12 cm
(d)
18 cm
Answer: (a) 8 cm
18. If angle between two radii of a circle is 130°, the angle between the tangents at the ends of the radii is
(a) 90°
(b) 50°
(c) 70°
(d)
40°
Answer: (b) 50°
19. A line intersecting a circle in two points is called a _______.
(a) Secant
(b) Chord
(c) Diameter
(d) Tangent
Answer: (a) Secant
20. In the figure below, the pair of tangents AP and AQ drawn from an external point A to a circle with centre O are perpendicular to each other and length of each tangent is 5 cm. Then the radius of the circle is
(a) 10 cm
(b) 7.5 cm
(c) 5 cm
(d) 2.5 cm
Answer: (c) 5 cm
21. A circle has centre O and radius 6 cm. If OP = 10 cm, then the
length of the tangent from P is
A) 6 cm
B) 8 cm
C) 10 cm
D) 12 cm
Answer: 8 cm
22. If two tangents inclined at an angle 60° are drawn to a circle of radius 3 cm, then length of each tangent is equal to
(a) (3/2)√3 cm
(b) 6 cm
(c) 3 cm
(d)
3√3 cm
Answer: (d) 3√3 cm
23. The tangent to a circle is ___________ to the radius through the point of contact.
(a) parallel
(b) perpendicular
(c) perpendicular bisector
(d) bisector
Answer: (b) perpendicular
24. In the figure below, PQ is a chord of a circle and PT is the tangent at P such that ∠QPT = 60°. Then ∠PRQ is equal to
(a) 135°
(b) 150°
(c) 120°
(d) 110°
Answer: (c) 120°
25. A circle has radius 10 cm. A tangent is drawn from a point at a distance of 26 cm from its centre. The length of the tangent is
A) 20 cm
B) 22 cm
C) 24 cm
D) 26 cm
Answer: 24 cm
26. In the below figure, if ∠AOB = 125°, then ∠COD is equal to
(a) 62.5°
(b) 45°
(c) 35°
(d) 55°
Answer: (d) 55°
Solution Hint: Angle subtended by the opposite sides of a quadrilateral circumscribing a circle at the centre of the circle are supplementry with each other.
27. The angle between a tangent and the radius at the point of contact
is
A) 30°
B) 60°
C) 90°
D) 120°
28. 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 ∠SQL = 50° and ∠SRM = 60°. Then ∠QSR is equal to
(a) 40°
(b) 60°
(c) 70°
(d)
80°
Answer: (c) 70°
29. Out of the two concentric circles, the radius of the outer circle is 5 cm and the chord AC of length 8 cm is a tangent to the inner circle. The radius of the inner circle will be
(a) 3 cm
(b) 4 cm
(c) 2.5 cm
(d) 2 cm
Answer: (a) 3 cm
30. The lengths of two tangents drawn from an external point to a circle are
A) unequal
B) equal
C) proportional
D) zero
Answer: (b)
31. In the given figure PA and PB are tangents to the circle with centre O. If ∠APB = 60°, then ∠OAB is
(a) 30°
(b) 60°
(c) 90°
(d) 15°
Ans: (a) 30°
Solution Hint: Angle made by the chord with the radius is double the angle between the radii.
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