1)

Chord AB of a circle is produced to a point P, and is a point on the circle such that PC is a tangent to the circle. If PC = 18 cm, and BP = 15 cm, then AB is equal to:

SSC CGL 2019

A)

5.8 cm

B)

6.2 cm

C)

6.6 cm

D)

8.5 cm

Correct Option: C

6.6 cm

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By the property,
\(PC^2 = PA \times PB;\)
\((18)^2 = PA \times 15;\)
PA = 324/15 = 21.6 cm;
AB = PA - PB = 21.6 - 15 = 6.6 cm

2)

Two parallel chords on the same side of the centre of a circle are 12 cm and 20 cm long and the radius of the circle is \(5\sqrt{13}cm\). What is the distance (in cm) between the chords?

SSC CGL 2019

A)

2

B)

3

C)

2.5

D)

1.5

3)

A circle touches the side BC of \(\triangle ABC\) at D and AB and AC are produced to E and F, respectively. If AB = 10 cm, AC = 8.6 cm and BC =6.4 cm, then BE =?

SSC CGL 2019

A)

3.2 cm

B)

3.5 cm

C)

2.2 cm

D)

2.5 cm

4)

In circle with centre O, AC and BD are two chords. AC and BD meet at E when produced. If AB is the diameter and \(\angle AEB=68^0\), then the measure of \(\angle DOC\) is :

SSC CGL 2019

A)

\(32^0\)

B)

\(30^0\)

C)

\(22^0\)

D)

\(44^0\)

5)

In a circle, AB and DC are two chords. When AB and DC are produced, they meet at P. If PC = 5.6 cm, PB = 6.3 cm and AB = 7.7 cm, then the length of CD is:

SSC CGL 2019

A)

8.35 cm.

B)

9 cm.

C)

10.15 cm.

D)

9.25 cm.