Geometry (Part-13)

Total Questions: 35

11. In a circle with centre O, Chord AB and diameter CD intersect each other at point E, inside the circle. If ∠AOD = 42º and ∠BOC = 104º then what is the measure (in degrees) of ∠AED? [SSC CHSL 04/08/2021 (Evening)]

1. (a) 73°
2. (b) 62°
3. (c) 58°
4. (d) 84°

Correct Answer: (a) 73°

Solution:

12. In an isosceles triangle ABC, AB = AC and AD is perpendicular to BC. If AD = 12 cm and the perimeter of of ∆ABC is 36 cm, then the length of BC (in cm) is: [SSC CHSL 05/08/2021 (Morning)]

1. (a) 5
2. (b) 12
3. (c) 10
4. (d) 13

Correct Answer: (c) 10

Solution:

13. The in-radius and circumradius of a right-angled triangle is 3 cm and 12.5 cm, respectively. The area of the triangle (in cm²) is: [SSC CHSL 05/08/2021 (Evening)]

1. (a) 64
2. (b) 48
3. (c) 88
4. (d) 84

Correct Answer: (d) 84

Solution:

14. Point A, B, C and D are concyclic points of a circle with centre O, such that ∠DOC = 73°. The measure of ∠AOC is 215°. What is the measure of ∠AOD? [SSC CHSL 06/08/2021 (Afternoon)]

1. (a) 145°
2. (b) 273°
3. (c) 87°
4. (d) 72°

Correct Answer: (d) 72°

Solution:

15. AB is the diameter of a circle of radius 9 cm. PQ is a chord (not a diameter) that intersects AB at M perpendicularly. If AM : BM = 5 : 4 then the length of chord PQ will be: [SSC CHSL 09/08/2021 (Afternoon)]

1. (a) 5√5
2. (b) 6√3
3. (c) 6√5
4. (d) 8√5

Correct Answer: (d) 8√5

Solution:

16. If the perimeter of an isosceles right triangle is 15(√2 + 1) cm, then the area of the triangle (in cm²) will be: [SSC CHSL 09/08/2021 ((Afternoon)]

1. (a) 46.5
2. (b) 45
3. (c) 56.25
4. (d) 55

Correct Answer: (c) 56.25

Solution:

17. If S is a point on side QR of a triangle PQR such that QS = 10 cm, QR = 18 cm and ∠PSR = ∠QPR, then the length of PR (in cm) will be: [SSC CHSL 10/08/2021 (Afternoon)]

1. (a) 16
2. (b) 12
3. (c) 15
4. (d) 14

Correct Answer: (b) 12

Solution:

18. In ∆PQR, QT⊥PR and S is a point on QR such that ∠PSQ = P°. If ∠TQR = 44° and ∠SPR = 32°, then the value of P is: [SSC CHSL 10/08/2021 (Evening)]

1. (a) 72°
2. (b) 82°
3. (c) 76°
4. (d) 78°

Correct Answer: (d) 78°

Solution:

19. The sides AB, BC and AC of ∆ABC are 12 cm, 8 cm and 10 cm, respectively. A circle is inscribed in the triangle touching AB, BC and AC at D, E and F respectively. The ratio of the lengths of AD to CE is: [SSC CHSL 10/08/2021 (Evening)]

1. (a) 5 : 7
2. (b) 3 : 5
3. (c) 10 : 7
4. (d) 7 : 3

Correct Answer: (d) 7 : 3

Solution:

20. From a point P, which is at a distance of 13 cm from the centre O of a circle, a pair of tangents PQ and PR of length 12 cm are drawn to the circle. The area of the quadrilateral PQOR is: [SSC CHSL 11/08/2021 (Morning)]

1. (a) 50
2. (b) 76
3. (c) 80
4. (d) 60

Correct Answer: (d) 60

Solution:

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