Geometry (Part-12)

Total Questions: 50

41. In triangle ABC, D is a point on BC such that BD : DC = 3 : 4. E is a point on AD such that AE : ED = 2 : 3. Find the ratio of area (∆ECD): area (ΔΑΕΒ). [SSC CGL 17/08/2021 (Evening)]

1. (a) 9 : 8
2. (b) 1 : 2
3. (c) 2 : 1
4. (d) 8 : 9

Correct Answer: (c) 2 : 1

Solution:

42. Point P lies outside a circle with centre O. Tangents PA and PB are drawn to meet the circle at A and B respectively. If ∠APB = 80°, then ∠OAB is equal to: [SSC CGL 18/08/2021 (Morning)]

1. (a) 140°
2. (b) 40°
3. (c) 70°
4. (d) 35°

Correct Answer: (b) 40°

Solution:

43. ΔABC~ ΔDEF If the areas of ΔABC and ΔDEF are 100 cm² and 81 cm², respectively and the altitude of ΔDEF is 6.3 cm, then the corresponding altitude (in cm) of ΔABC is: [SSC CGL 18/08/2021 (Morning)]

1. (a) 5.6
2. (b) 9
3. (c) 7
4. (d) 8.4

Correct Answer: (c) 7

Solution:

44. ∆ABC is an equilateral triangle. D is a point on side BC such that BD : BC = 1 : 3. If AD = 5√7cm, then the side of the triangle is: [SSC CGL 18/08/2021 (Afternoon)]

1. (a) 18cm
2. (b) 12cm
3. (c) 20cm
4. (d) 15cm

Correct Answer: (d) 15cm

Solution:

45. In a trapezium PQRS, PQ is parallel to RS and diagonal PR and QS intersect at O. PQ = 4 cm, SR = 10cm, then what is area (∆POQ) : area (∆SOR)? [SSC CGL 18/08/2021 (Afternoon)]

1. (a) 4 : 25
2. (b) 2 : 3
3. (c) 4 : 9
4. (d) 2 : 5

Correct Answer: (a) 4 : 25

Solution:

46. A chord AB of circle C₁ of radius 17 cm touches circle C₂ which is concentric to C₁. The radius of C₂ is 8 cm. What is the length (in cm) of AB? [SSC CGL 18/08/2021 (Afternoon)]

1. (a) 30
2. (b) 25
3. (c) 20
4. (d) 24

Correct Answer: (a) 30

Solution:

47. In a right angled triangle ABC, the lengths of the sides containing the right angle are 5 cm and 12 cm respectively. A circle is inscribed in the triangle ABC. What is the radius of the circle (in cm)? [SSC CGL 18/08/2021 (Evening)]

1. (a) 2.8
2. (b) 3
3. (c) 2
4. (d) 2.5

Correct Answer: (c) 2

Solution:

48. Points A and B are on a circle with centre O. Point C is on the major arc АВ. If ∠OAC = 35° and ∠OBC = 45°, then what is the measure (in degrees) of the angle subtended by the minor arc AB at the centre? [SSC CGL 18/08/2021 (Evening)]

1. (a) 80
2. (b) 70
3. (c) 100
4. (d) 160

Correct Answer: (d) 160

Solution:

49. Triangle ABC is an equilateral triangle. D and E are points on AB and AC respectively such that DE is parallel to BC and is equal to half the length of BC. If AD + CE + BC = 30 cm, then find the perimeter (in cm) of the quadrilateral BCED. [SSC CGL 20/08/2021 (Morning)]

1. (a) 45
2. (b) 25
3. (c) 37.5
4. (d) 35

Correct Answer: (c) 37.5

Solution:

50. The angles of a triangle are in AP (arithmetic progression). If measure of the smallest angle is 50° less than that of the largest angle, then find the largest angle (in degrees) [SSC CGL 20/08/2021 (Afternoon)]

1. (a) 80
2. (b) 85
3. (c) 90
4. (d) 75

Correct Answer: (b) 85

Solution:

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