Geometry (Part-3)

Total Questions: 50

41. If the sum of two sides of an equilateral triangle is 16 cm, then find the third side. [SSC CGL 09/09/2024 (1st Shift)]

Correct Answer: (d) 8 cm
Solution:Let the side of an equilateral triangle be x
According to the questions,
2x = 16 ⇒ x = 8cm
We know that an equilateral triangle all side equal to each other so the third side will be 8cm.

42. Let O be the centre of the circle and AB and CD are two parallel chords on the same side of the radius. OP is perpendicular to AB and OQ is perpendicular to CD. If AB = 10 cm, CD = 24 cm and PQ = 7 cm, then the diameter (in cm) of the circle is equal to: [SSC CGL 09/09/2024 (1st Shift)]

Correct Answer: (a) 26
Solution:

43. The distance between the centres of two circles of radii 22 cm and 10 cm is 37 cm. If the points of contact of a direct common tangent to these circles are M and Q, then find the length of the line segment MQ. [SSC CGL 09/09/2024 (1st Shift)]

Correct Answer: (a) 35 cm
Solution:

44. The points P and S are on the same side of the line segment QR, such that ∠PQR = 90°, ∠SRQ = 90° and PQ = SR. Select the correct statement. [SSC CGL 09/09/2024 (2nd Shift)]

Correct Answer: (d) ∆PQR ≅ ∆SRQ by SAS
Solution:

45. The angles of triangle are such that one is average of other two, then the angles are: [SSC CGL 09/09/2024 (2nd Shift)]

Correct Answer: (d) 1
Solution:

46. Let C be a circle with centre O and P be an external point to C. Let PA and PB be two tangents to C with A and B being the points of tangency, respectively. If PA and PB are inclined to each other at an angle of 60°, then find ∠POA. [SSC CGL 09/09/2024 (2nd Shift)]

Correct Answer: (b) 60°
Solution:

47. Two triangles EFG and HIJ are congruent. If the area of ∆EFG is 124cm², then the area of ∆HIJ will be: [SSC CGL 09/09/2024 (3rd Shift)]

Correct Answer: (a) 124 cm²
Solution:Concept :- congruent triangles always have the same area. Hence, ar∆HIJ = ar∆EFG = 124cm²

48. By applying which of the following criteria can two triangles NOT be proved congruent? [SSC CGL 10/09/2024 (1st Shift)]

Correct Answer: (b) angle-angle-angle
Solution:Applying angle-angle-angle (AAA) criteria, two triangle can never be proved congruent.

49. Two circles of radii 18 cm and 12 cm touch each other externally. Find the length (in cm) of their direct common tangent. [SSC CGL 10/09/2024 (1st Shift)]

Correct Answer: (c) 12√6
Solution:

50. The side of an equilateral triangle is 28 cm. Taking each vertex as the centre, a circle is described with a radius equal to half the length of the side of the triangle. Find the area of that part of the triangle which is not included in the circles (use π = 22/7 and √3 = 1.73 ) [SSC CGL 10/09/2024 (1st Shift)]

Correct Answer: (c) 31.08 cm²
Solution: