Geometry (Part-3)

Total Questions: 50

21. ABCD is a cyclic quadrilateral whose diagonals intersect at P. If AB = BC, ∠DBC = 70° and ∠BAC = 30°, then the measure of ∠PCD is: [SSC CGL 06/06/2019 (Morning)]

1. (a) 35°
2. (b) 50°
3. (c) 55°
4. (d) 30°

Correct Answer: (b) 50°

Solution:

22. ABCD is a cyclic quadrilateral in which ∠A = 67° and ∠B = 92°. What is the difference between the measure of ∠Cand ∠D? [SSC CGL 04/06/2019 (Evening)]

1. (a) 29°
2. (b) 27°
3. (c) 19°
4. (d) 25°

Correct Answer: (d) 25°

Solution:

23. In ΔABC, AD ⊥ BC and BE ⊥ AC, AD and BE intersect each other at F. If BF = AC, then the measure of ∠ABC is: [SSC CGL 04/06/2019 (Afternoon)]

1. (a) 45°
2. (b) 60°
3. (c) 70°
4. (d) 50°

Correct Answer: (a) 45°

Solution:

24. A triangle ABC is inscribed in a circle with centre O. AO is produced to meet the circle at K and AD ⊥ BC. If ∠B = 80° and ∠C = 64°, then the measure of ∠DAK is: [SSC CGL 04/06/2019 (Afternoon)]

1. (a) 10°
2. (b) 16°
3. (c) 12°
4. (d) 20°

Correct Answer: (b) 16°

Solution:

25. In a circle of radius 10 cm, with centre O, PQ and PR are two chords each of length 12 cm. PO bisects chord QR at the points S. The length of OS (in cm): [SSC CGL 04/06/2019 (Morning)]

1. (a) 2.8
2. (b) 2.5
3. (c) 3.2
4. (d) 3

Correct Answer: (a) 2.8

Solution:

26. In ΔABC, F and E are the points on sides AB and AC respectively, such that FE || BC and FE divide the triangle in two parts of equal area. If AD ⊥ BC and AD intersect FE at G, then GD:AG = ? [SSC CGL 04/06/2019 (Morning)]

1. (a) √2 : 1
2. (b) (√2-1) : 1
3. (b) 2√2 : 1
4. (d) (2+1) : 1

Correct Answer: (b) (√2-1) : 1

Solution:

27. A circle is inscribed in a triangle ABC. It touches the sides AB, BC and AC at the points R, P and Q respectively. If AQ = 4.5 cm, PC = 5.5 cm and BR = 6 cm, then the perimeter of the triangle ABC is: [SSC CGL 04/06/2019 (Morning)]

1. (a) 30.5
2. (b) 28
3. (c) 32
4. (d) 26.5

Correct Answer: (c) 32

Solution:

28. A unique circle can always be drawn through x number of given non-collinear points, then x must be: [SSC CPO 16/03/2019 (Evening)]

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

Correct Answer: (b) 3

Solution:Short-Trick: To draw a unique circle it is always required to have three non-collinear points.

29. Side AB of a triangle ABC is 80 cm long, whose perimeter is 170 cm. If angle ABC = 60°, the shortest side of triangle ABC measures, ____cm. [SSC CPO 16/03/2019 (Evening)]

1. (a) 17
2. (b) 15
3. (c) 25
4. (d) 21

Correct Answer: (a) 17

Solution:

30. Which of the following solids has the least number of faces? [SSC CPO 15/03/2019 (Morning)]

1. (a) Cube
2. (b) Cone
3. (c) Triangular prism
4. (d) Square pyramid

Correct Answer: (b) Cone

Solution:Cone has only two faces. Rest have more than two faces each.

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