Geometry (Part-2)

Total Questions: 50

1. Two circles touch each other externally at P. AB is a direct common tangent to the two circles, A and B are points of contact, and ∠PAB = 40°. The measure of ∠ABP is: [SSC CGL 01/12/2022 (1st Shift)]

1. (a) 45°
2. (b) 55°
3. (c) 50°
4. (d) 40°

Correct Answer: (c) 50°

Solution:

2. In the given figure, MNP, SQP, NQR and MSR are straight lines. ∠NPQ = 54° and ∠QRS = 68°. What is the degree measure of ∠SMN ? [SSC CPO 10/11/2022 (Evening)]

1. (a) 29°
2. (b) 38°
3. (c) 54°
4. (d) 68°

Correct Answer: (a) 29°

Solution:

3. PQ and RS are two parallel chords of a circle such that PQ is 48 cm and RS is 40 cm. If the chords are on the opposite sides of the centre and the distance between them is 22 cm, what is the radius (in cm) of the circle? [SSC CPO 09/11/2022 (Afternoon)]

1. (a) 25
2. (b) 24
3. (c) 35
4. (d) 22

Correct Answer: (a) 25

Solution:

4. An arc on a circle that is 15 cm long subtends a 24° angle at the centre. What is the circumference of the circle? [SSC CHSL 02/06/2022 (Afternoon)]

1. (a) 240 cm
2. (b) 220 cm
3. (c) 236 cm
4. (d) 225 cm

Correct Answer: (d) 225 cm

Solution:

5. Calculate the area of the quadrilateral formed with the vertices (-3, 2), (5, 4), (7, -6) and (-5, -4). [SSC CHSL 27/05/2022 (Morning)]

1. (a) 80 square units
2. (b) 160 square units
3. (c) 0 square units
4. (d) 150 square units

Correct Answer: (a) 80 square units

Solution:

6. In the following figure, P and Q are centers of two circles. The circles are intersecting at points A and B. PAproduced on both the sides meets the circles at C and D. If ∠CPB = 100° , then find the value of x. [SSC CGL 18/04/2022 (Morning)]

1. (a) 115
2. (b) 120
3. (c) 110
4. (d) 100

Correct Answer: (d) 100

Solution:

7. An isosceles △MNP is inscribed in a circle. If MN = MP = 16√5 cm, and NP = 32 cm what is the radius (in cm) of the circle? [SSC CGL 13/04/2022 (Evening)]

1. (a) 20
2. (b) 18√5
3. (c) 18
4. (d) 20√5

Correct Answer: (a) 20

Solution:

8. In triangle ABC, D and E are points on BC such that AD = AE and ∠BAD = ∠CAE If AB = (2p+3) , BD = 2p , AC =(3q-1) and CE = q, then find the value of (p+q) . [SSC CGL 13/04/2022 (Morning)]

1. (a) 3
2. (b) 4.5
3. (c) 3.6
4. (d) 2

Correct Answer: (a) 3

Solution:

9. In a circle with centre O, AC and BD are two chords. AC and BD meet at E, when produced. If AB is a diameter and ∠AEB = 36º , then the measure of ∠DOC is: [SSC CGL 12/04/2022 (Evening)]

1. (a) 112°
2. (b) 124°
3. (c) 136°
4. (d) 108°

Correct Answer: (d) 108°

Solution:

10. AB is a chord in the minor segment of a circle with center O. C is a point on the minor arc (between A and B). The tangents to the circle at A and B meet at a point P. If ∠ACB = 108° , then ∠APB is equal to: [SSC CGL Tier II (03/02/2022)]

1. (a) 36°
2. (b) 54°
3. (c) 27°
4. (d) 18°

Correct Answer: (a) 36°

Solution:

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