Geometry (Railway Maths) (Part – VI)

Total Questions: 50

41. In the given figure, AB is the diameter of the circle. AP is a tangent to circle at A. Extended BC meets thetangent at P. <AOC = 36⁰. Find <BPQ. [RRB NTPC 01/04/2021 (Morning) ]

Correct Answer: (c) 108⁰
Solution:

42. In the above figure, BO and CO are the angular bisectors of <DBC and <BCE respectively. The measure of x is ______. [RRB NTPC 01/04/2021 (Evening) ]

Correct Answer: (c) 64°
Solution:

43. AB and CD are two chords of a circle. AB = 6 cm, CD = 8 cm and AB || CD. If the distance between AB and CD is 7 cm and the center of the circle lies in the interior of the quadrilateral ABCD, then find the radius of the circle (in cm). [RRB NTPC 03/04/2021 (Morning)]

Correct Answer: (a) 5
Solution:

44. AB is the diameter of a semicircle. C is a point on line AB, AC = 6 cm, D is the point on the semicircle such that CD is perpendicular to AB and CD = 9 cm. Find the diameter of the semicircle. [RRB NTPC 03/04/2021 (Morning)]

Correct Answer: (d) 19.5 cm
Solution:

45. In the given figure, A, B and C are three points on a circle. If AB = 3 cm and BC = 4 cm, then the measure of the radius of the circle is: [RRB NTPC 06/04/2021 (Evening) ]

Correct Answer: (d) 5/2 cm
Solution:

46. Which of the following statements is correct? [RRB NTPC 07/04/2021 (Evening) ]

1 .The angle between two tangents to a circle may be 0⁰.
2 .If a transversal intersects two lines such that a pair of alternate interior angles is equal, then the two lines are parallel.
3 .The tangents at the end points of a diameter of a circle are perpendicular.

Correct Answer: (b) Both 1 and 2, but not 3
Solution:

Statement 1 and 2 is true.

47. In an isosceles ∆ABC, if the measure of ∠A is twice that of the base ∠B, then the measure of ∠C will be: [RRB NTPC 08/04/2021 (Morning)]

Correct Answer: (a) 45°
Solution:

48. The sum of the consecutive angles of a parallelogram is equal to: [RRB NTPC 08/04/2021 (Morning)]

Correct Answer: (d) 180°
Solution:

The sum of the consecutive angles of a parallelogram is equal to 180°

49. Circles are inscribed and circumscribed to a triangle whose sides are 3 cm, 4 cm, and 5 cm. What is the ratio of radius of the in-circle to that of the circumcircle? [RRB NTPC 08/04/2021 (Evening)]

Correct Answer: (c) 2 : 5
Solution:

50. In the given figure, AB and CD are parallel lines. O is a point such that angle CDO = 70⁰ and angle DOB = 100⁰. Find angle ABO. [RRB NTPC 08/04/2021 (Evening) ]

Correct Answer: (c) 30⁰
Solution: