Geometry (Part-7)

Total Questions: 50

31. E, F, G, and H are four points lying on the circumference of a circle to make a cyclic quadrilateral. If ∠FGH = 57°, then what will be the measure of the ∠HEF? [SSC CPO 04/10/2023 (1st Shift)]

Correct Answer: (c) 123°
Solution:

32. In a ∆PQR, ∠P : ∠Q : ∠R = 3 : 4 : 8. The shortest side and the longest side of the triangle, respectively, are: [SSC CPO 04/10/2023 (2nd Shift)]

Correct Answer: (d) QR and PQ
Solution:

33. In a triangle ABC, if ∠B = 90º, ∠C = 45° and AC = 4 cm, then the value of BC is: [SSC CPO 04/10/2023 (2nd Shift)]

Correct Answer: (b) 2√2 cm
Solution:

34. Find the area of a triangle whose length of two sides are 4 cm and 5 cm and the angle between them is 45°. [SSC CPO 04/10/2023 (2nd Shift)]

Correct Answer: (d) 5√2 cm²
Solution:

35. Let ABC, PQR be two congruent triangles such that ∠A= ∠P = 90º. If BC = 17 cm, PR = 8 cm, find AB (in cm). [SSC CPO 04/10/2023 (2nd Shift)]

Correct Answer: (d) 15
Solution:

Pythagorean triples (8,15,17)
And ∆ABC and ∆PQR are the congruent
triangles so the length of AB will be 15

36. Out of two concentric circles, the radius of the outer circle is 6 cm and the chord PQ of the length 10 cm is a tangent to the inner circle. Find the radius (in cm) of the inner circle. [SSC CPO 05/10/2023 (2nd Shift)]

Correct Answer: (a) √11
Solution:

37. The chord of a circle is equal to its radius. Find the difference between the angle subtended by this chord at the minor arc and major arc of the circle. [SSC CPO 05/10/2023 (3rd Shift)]

Correct Answer: (b) 120°
Solution:

38. In ∆ABC with sides 8 cm, 9 cm and 12 cm, the angle bisector of the largest angle divides the opposite sides into two segments. What is the length of the shorter segment? [SSC CPO 05/10/2023 (3rd Shift)]

Correct Answer: (a)
Solution:

39. A tangent AB at point A of a circle of radius 6 cm meets a line through the centre O at point B. If OB = 10 cm, then the length of AB (in cm) is equal to: [SSC CHSL 02/08/2023 (1st Shift)]

Correct Answer: (d) 8
Solution:

40. Which of the following sets of angles forms a triangle? [SSC CHSL 02/08/2023 (2nd Shift)]

Correct Answer: (c) 60°, 40°, 80°
Solution:

Sum of all angles of a triangle = 180º
Only one options (c) is possible i.e 60°, 40° and 80°