151)

Two equal circles of radius 8 cm intersect each other in such a way that each passes through the centre of the other. The length of the common chord is:

SSC CGL 2022

A)

\(2\sqrt3\)

B)

\(\sqrt 3 \)

C)

\(8\sqrt3 cm \)

D)

\(4\sqrt3\)

152)

A chord of length 42 cm is drawn in a circle of diameter 58 cm. Another chord of length 40 cm is drawn parallel to the chord of length 42 cm. Find the difference between the distances of the two chords from the centre.

SSC CGL 2022

A)

3 cm

B)

1 cm

C)

4 cm

D)

2 cm

153)

The length of the chord of a circle is 24 cm, and the perpendicular distance between the centre and the chord is 5 cm. The radius of the circle is:

SSC CGL 2022

A)

12 cm

B)

13 cm

C)

10 cm

D)

24 cm

154)

Select the INCORRECT statement with respect to the properties of a circle.

SSC CGL 2022

A)

The diameter of a circle is the longest chord of a circle.

B)

The radius drawn perpendicular to a chord bisects the chord.

C)

Two tangents drawn at the end of the diameter of a circle are parallel.

D)

The perpendicular distance from the centre of a circle increases when the length of a chord increases.

155)

The circumference of the two circles is 110 cm and 330 cm respectively. What is the difference between their radii?

SSC CGL 2022

A)

46 cm

B)

15 cm

C)

70 cm

D)

35 cm

156)

The hour hand moves through 4 hours and has a length of 6 cm. Find the area (in cm², rounded off to two decimal places) of the sector covered by the hour hand.

SSC CGL 2022

A)

37.71

B)

30.67

C)

32.69

D)

35.75

157)

Radius of a circle is 5 cm. Length of chord AB in this circle is 6 cm. What is the distance of this chord from the centre of the circle?

SSC CGL 2022

A)

6 cm

B)

5 cm

C)

4 cm

D)

8 cm

158)

If C₁, C₂ be the centres of two circles and r₁, r₂ be the respective radii such that the distance between the centres is equal to the sum of the radii of the two circles, find the number of common tangents.

SSC CGL 2022

A)

1

B)

2

C)

4

D)

3

159)

If two circles of radii 18 cm and 8 cm touch externally, then the length of a direct common tangent is:

SSC CGL 2022

A)

16 cm

B)

14 cm

C)

24 cm

D)

12 cm

160)

The diameters of two circles are 12 cm and 20 cm, respectively and the distance between their centres is 16 cm. Find the number of common tangents to the circles.

SSC CGL 2022

A)

1

B)

3

C)

2

D)

4