Geometry (Part-7)

Total Questions: 50

41. Two triangles MNO and XYZ are given similar with the ratio of their side as 9:4. If the area of the larger triangle is 243 sq.cm, then the area of smaller triangle will be: [SSC CHSL 02/08/2023 (3rd Shift)]

Correct Answer: (c) 48 sq.cm
Solution:

42. In a circle of radius 14 cm, an arc subtends an angle of 90° at the centre. The length of arc (in cm) is equal to: (Take π= 22/)7 [SSC CHSL 02/08/2023 (3rd Shift)]

Correct Answer: (a) 22
Solution:

43. AB is a chord of the circle and AOC is its diameter such that angle ACB = 65°. If AT is the tangent to the circle at the point A, then angle BAT is equal to: [SSC CHSL 02/08/2023 (4th Shift)]

Correct Answer: (a) 65°
Solution:

Alternate segament theorem :-
In any circle, the angle between a chord
and a tangent through one of the endpoints
of the chord is equal to the angle made by the
same chord in the alternate segament

44. ∆PQR and ∆SQR are both isosceles triangles on a common base QR such that P and S lie on the same side of QR. If ∠QSR = 60° and ∠QPR = 100°, then find ∠SRP. [SSC CHSL 03/08/2023 (1st Shift)]

Correct Answer: (d) 20°
Solution:

45. Which option with given sides forms a Triangle? [SSC CHSL 03/08/2023 (2nd Shift)]

Correct Answer: (a) 8, 6, 9
Solution:

46. In a triangle PQR, QR is produced to S. If ∠PRS = (9x - 15)º, ∠RPQ = (2x)º and ∠PQR = (4x + 15)º, what is the value of x ? [SSC CHSL 03/08/2023 (3rd Shift)]

Correct Answer: (c) 10°
Solution:

47. If in ∆PQR and ∆DEF, ∠P = 52º, ∠Q = 74º, ∠R = 54º, ∠D = 54º, ∠E = 74º, and ∠F = 52º, then which of the following is correct? [SSC CHSL 03/08/2023 (3rd Shift)]

Correct Answer: (a) ∆PQR ~ ∆FED
Solution:

∠P = ∠F = 52º, ∠Q = ∠E = 74º
∠R = ∠D = 54º
So, ∆PQR ~ ∆FED

48. Minor arc BC subtends angles BAC and BDC at points A and D, respectively, on the circumference in the major sector of the circle with centre O. What is the value (in degrees) of (∠ABC + ∠ACB), if ∠BDC = 73º ? [SSC CHSL 03/08/2023 (4th Shift)]

Correct Answer: (b) 107°
Solution:

49. In ∆ABC, the internal bisectors of ∠ABC and ∠ACB meet at X and ∠BAC = 30°. The measure of ∠BXC is: [SSC CHSL 03/08/2023 (4th Shift)]

Correct Answer: (c) 105°
Solution:

50. In triangle RST, M and N are two points on RS and RT such that MN is parallel to the base ST of the triangle RST. If RM = 1/3 MS, and ST = 5.6 cm, what is the ratio of Area of Triangle RMN/Area of Trapezium MNST ? [SSC CHSL 04/08/2023 (1st Shift)]

Correct Answer: (c) 1/15
Solution: