MULTIPLE CHOICE QUESTIONS: (MCQ’s).
1. A circle has a ______number of tangents .
(a) 0
(b) 1
(c) 2
(d) Infinite
2. The common point of the tangent and the circle is called the _____ .
(a) Point of contact
(b) Point of meeting
(c) Centre of circle
(d) None of the above
3. A circle can have _____ parallel tangents at a single time.
(a) One
(b) Two
(c) Three
(d) Four
4. 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
(d) 40º
5. 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
6. 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°
7. 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
8. If a parallelogram circumscribes a circle, then it is a____
(a) Square
(b) Rectangle
(c) Rhombus
(d) None of the above
9. 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
(b) 10
(c) 12
(d) 18
10. Circles of this types are called _____
(a) Circular
(b) Concentric
(c) Normal
(d) None of the above
11. A line that intersects the circle at one point only is called ____
(a) Secant
(b) Chord
(c) Radius
(d) Tangent
12. The length of the tangent drawn from an external point to a circle are ____
(a) Equal
(b) Similar
(c) Not equal
(d) Parallel
13. The tangents drawn at the ends of the diameter of the circle are ____
(a) Equal
(b) Similar
(c) Not equal
(d) Parallel
14. The tangent to a circle is _____ the radius through the point of contact
(a) Equal
(b) Perpendicular
(c) Parallel
(d) None of the above
15. The parallelogram subscribing a circle is a ___
(a) Square
(b) Rectangle
(c) Rhombus
(d) Kite
16. If radii of two concentric circles are 4 cm and 5 cm, then the length of each chord of one circle which is tangent to the other circle is_____
(a) 3 cm
(b) 6 cm
(c) 9 cm
(d) 1 cm
17. In Fig., if ∠AOB = 125°, then ∠COD is equal to _____
(a) 62.5°
(b) 45°
(c) 35°
(d) 55°
18. If Fig., AB is a chord of the circle and AOC is its diameter such that ∠ACB = 50°. If AT is the tangent to the circle at the point A, the ∠BAT is equal to ____
(a) 65°
(b) 60°
(c) 50°
(d) 40°
19. From a point P which is at a distance of 13 cm from the point O of a circle of radius 5 cm, the pair of tangents PQ and PR to the circle are drawn. Then the area of the quadrilateral PQOR is ___
(a) 60 cm²
(b) 65 cm²
(c) 30 cm²
(d) 32.5 cm²
20. At one end A of a diameter AB of a circle of radius 5 cm, tangent XAY is drawn to the circle. The length of the chord CD parallel to XY and at a distance 8 cm from A is ___
(a) 4 cm
(b) 5 cm
(c) 6 cm
(d) 8 cm
21. In Fig., AT is a tangent to the circle with centre O such that OT = 4 cm and ∠OTA = 30°. Then AT is equal to ____
(a) 4 cm
(b) 2 cm
(c) 2√3 cm
(d) 4√3 cm
22. In Fig., if O is the centre of a circle PQ is a chord and the tangent PR at P makes an angle of 50° with PQ, then ∠POQ is equal to ____
(a) 100°
(b) 80°
(c) 90°
(d) 75°
23. In Fig., if PA and PB are tangents to the circle with centre 0 such that ∠APB = 50°, then ∠AOB is equal to ____
(a) 25°
(b) 130°
(c) 100°
(d) 50°
24. Tangents SP and SQ from a point S to a circle with centre O are inclined to each other at an angle of 110° then ∠SOP = ____
(a) 35°
(b) 130°
(c) 70°
(d) 50°
25. If PA and PS are two tangents to a circle with centre O such that
∠APB = 62° then ∠AOB = ____
(a) 135°
(b) 180°
(c) 70°
(d) 118°
26. In Fig., if ∠AOB = 125°, and ∠COD = 55°. Then ∠AOD + ∠BOC = ____
(a) 90°
(b) 45°
(c) 120°
(d) 180°
27. A point P is 13 cm from the centre of the circle.The length of the tangent drawn from P to the circle is 12 cm. The radius of the circle is ____
(a) 9
(b) 5
(c) 12
(d) 8
28. A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm.Length of PQ will be _____
(a) 90
(b) 45
(c) √119
(d) √112
29. One of the two concentric circle is of radii 5 cm . The length of the chord of the larger circle which touches the smaller circle is 8 cm. Radii of other circle is ____
(a) 9
(b) 5
(c) 3
(d) 8
30. If Fig., AB is a chord of the circle and AOC is its diameter such that ∠ACB = 50°. If AT is the tangent at the point A, and ∠BAT = 50° .Then ∠COA = _____
(a) 180°
(b) 160°
(c) 150°
(d) 110°
31. At one end A of a diameter AB of a circle a tangent XAY is drawn to the circle. The length of the chord CD parallel to XY and at a distance 8 cm from A is 8 cm .The radius of the circle =___
(a) 4 cm
(b) 5 cm
(c) 6 cm
(d) 8 cm
32. AT is a tangent to the circle with centre O such that OT = 4 cm and ∠OTA = 30°. And AT = 4√3 cm. Join OA .Then ∠TOA = ____
(a) 60°
(b) 120°
(c) 45°
(d) 70°
33. In Fig., if PA and PB are tangents to the circle with centre O such that ∠APB = 50°, tand ∠AOB = 130°. Then ∠OAB = ___
(a) 25°
(b) 30°
(c)10°
(d) 50°
34. In Fig., if O is the centre of a circle PQ is a chord and the tangent PR at P makes an angle of 50° with PQ, and ∠POQ = 100°. Then ∠OPQ = ____
(a) 100°
(b) 80°
(c) 90°
(d) 40°
35. Two or more circles having a common radius are called as _____ circles.
(a) Circular
(b) Concentric
(c) Normal
(d) None of the above
1 :(d) ⇒ Textbook (Ex 10.1)
2 :(a) ⇒ Textbook ( Activity 2)
3 :(b) ⇒ Textbook (Ex 10.1)
4 :(a) ⇒ (Theorem 10.1)
5 :(c) ⇒ OA is the longest side.
6 :(b) ⇒ ∠POQ + ∠OPT + ∠OQT + ∠PQT = 360°
7 :(a) ⇒ Draw the fig and use Pythagoras theorem
8 :(c) ⇒ Tangents to a circle from an external point are equal
9 :(a) ⇒ Textbook (Example 1)
10 :(b) ⇒ Circles having common radius
11 :(d) ⇒ Definition tangent
12 :(a) ⇒ Textbook ( theorem 10.2)
13 :(d) ⇒ Draw and see
14 :(b) ⇒ Draw and see
15 :(c) ⇒ Textbook (example 10.2)
16 :(b) ⇒ Radius of bigger circle + difference of radius
17 :(d) ⇒ ∠AOB + ∠COD = 180°
18 :(c) ⇒ ∠ACB +∠ CBA +∠ BAC = 180° and∠ BAC +∠ BAT = 90°
19 :(a) ⇒ OP =13 cm ,OQ = OR = 5cm .Find area of the two Δs and add them
20 :(d) ⇒ Draw the fig .Let centre of CD be M and OM = 3 cm , OD = 5 cm (radius)
21 :(d) ⇒ Tan 30° = 4/x . So x = ?
22 :(a) ⇒ ∠ OPQ =∠ OQP = 40° and ΔPOQ is isosceles
23 :(b) ⇒ ∠ APB +∠POB = 180°
24 : (a) ⇒ ∠PSQ = 110° and so ∠POQ = 70° and …..
25 : (d) ⇒ ∠APB = 62° and so ∠AOB = 180°− 62 °
26: (d) ⇒ Angles around a point is equal to 360°
27: (b) ⇒ OP = √PQ²−OQ²
28: (c) ⇒ PQ = √ OQ²− PQ²
29: (c) ⇒ The chord AB touches the smaller circle at P. And OA² = OP² + AP²
30: (a) ⇒ AOC is its diameter
31: (b) ⇒ Draw the fig .Let centre of CD be M and OM = 3 cm , OD = 5 cm (radius)
32: (a) ⇒ OAT is a triangle and ∠OAT = 90°
33: (a) ⇒ OAB is a triangle. And ∠ OAB = ∠OBA
34: (d) ⇒ ∠OPR = 90°
35: (b) ⇒ Concentric circles definition