Geometry (Part-9)

Total Questions: 50

1. ∆ABC inscribe in a circle with center O. If AB = 9 cm, BC = 40 cm and AC = 41 cm, then what is the circum-radius of a triangle? [SSC CHSL 17/08/2023 (4th Shift)]

Correct Answer: (a)
Solution:

2. The perimeters of two similar triangles XYZ and PQR are respectively 62 cm and 42 cm. If PQ = 21 cm, find XY? [SSC CHSL 17/08/2023 (4th Shift)]

Correct Answer: (d) 31cm
Solution:

3. Two concentric circles are of radii 10 cm and 6 cm. Find the length of the chord of the larger circle which touches the smaller circle. [SSC CGL 14/07/2023 (1st shift)]

Correct Answer: (b) 16 cm
Solution:

4. Which of the following statements is INCORRECT? [SSC CGL 14/07/2023 (3rd shift)]

Correct Answer: (c) A line which intersects two distinct points of a circle is called tangent.
Solution:

A line which intersects a circle at two distinct points is chord.
While tangent touches a circle only at one point.

5. If ∆XYZ ≅ ∆LMR then m + x + p = ________ . [SSC CGL 14/07/2023 (4th shift)]

Correct Answer: (c) 9
Solution:

6. The lengths of the three sides of a triangle are 30 cm, 42 cm and x cm. Which of the following is correct? [SSC CGL 17/07/2023 (2nd shift)]

Correct Answer: (c) 12 < x < 72
Solution:

Let the length of third side of triangle = x
The 3rd side of the triangle is always greater than the diffrence of the other two sides and less than the sum of the other two sides.
Then, (42 - 30) < x < (42 + 30 = 12 < x < 72

7. Which of the following statements is INCORRECT? [SSC CGL 17/07/2023 (4th shift)]

Correct Answer: (a) Radius is the longest chord of a circle.
Solution:

By checking the option, Radius is the longest chord of a circle (wrong)
Diameter is the longest chord of a circles.

8. Let A, B, C be the mid-points of sides PQ, QR and PR, respectively, of ∆PQR. If the area of ∆PQR is 32cm², then find the area (in cm²) of ∆АВС. [SSC CGL 18/07/2023 (1st shift)]

Correct Answer: (d) 8
Solution:

9. D and E points on the sides AB and AC, respectively, of ∆ABC such that DE is parallel to BC and AD:DB = 7 : 9. If CD and BE intersect each other at F, then find the ratio of areas of ∆DEF and ∆CBF. [SSC CGL 18/07/2023 (3rd shift)]

Correct Answer: (c) 49 : 256
Solution:

10. If in ΔΧΥΖ, XY = 4 and Xz = 5 cm and Q is a point on YZ such that XQ bisects ∠X, then YQ: QZ is: [SSC CGL 18/07/2023 (3rd shift)]

Correct Answer: (d) 4 : 5
Solution: