1)In the figure, PA is a tangent from an external point P to the circle with centre O. If \(\angle POB = 110 ^{\circ}\), then measure of \(\angle APO\) is:

SSC CGL 2020

Correct Option: C

\(20 ^{\circ}\)

PA is a tangent

\(\angle POA =180^{\circ}- 110 ^{\circ}=70^{\circ}\)

\(\angle PAO =90^{\circ}\)

\(\angle APO =180^{\circ}- 70 ^{\circ}-90^{\circ}=20^{\circ}\)

Class 10 Maths2)If angle of sector is 60°, radius is 3.5 cm then length of the arc is

Correct Option: A

3.66 cm

SSC CGL 20193)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:

Correct Option: C

6.6 cm

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

SSC CGL 20194)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?

Correct Option: A

2

SSC CGL 20195)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 =?

Correct Option: D

2.5 cm

SSC CGL 20196)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 :

Correct Option: D

\(44^0\)

SSC CGL 20197)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:

Correct Option: C

10.15 cm.

SSC CGL 20208)In a circle, chords PQ and TS are produced to meet at R. If RQ = 14.4 cm, PQ = 11.2 cm, and SR = 12.8 cm, then the length of chord TS is:

Correct Option: D

16 cm

RQ X PR = RS X TR; 14.4 X (14.4+11.2) = 12.8 X TR; TR = \({14.4\times25.6\over12.8}=28.8 cm\) ; TS = TR - SR = (28.8 - 12.8) cm = 16 cm

SSC CGL 20209)From an external point P, a tangent PQ is drawn to a circle, with the centre O, touching the circle at Q. If the distance of P from the centre is 13 cm and length of the tangent PQ is 12 cm, then the radius of the circle is:

Correct Option: C

5 cm

\triangle OPQ is a right angle triangle because \(\angle Q = 90^0\),

By Pythagoras,

\((OQ)^2 + (PQ)^2 = (OP)^2\);

\((OQ)^2 = (13)^2 - (12)^2\);

\((OQ)^2\) = 169 - 144;

\((OQ)^2\) = 25;

OQ = 5 cm.

SSC CGL 202010)In a circle, AB is a the diameter and CD is a chord. AB and CD produced meet at a point P, outside the circle. If PD = 15.3 cm, CD = 11.9 cm and AP = 30.6 cm,then the radius of the circle is is:

Correct Option: B

8.5 cm

From the property,

\(PA \times PB = PC \times PD\);

\(30.6 \times PB = (PD + CD) \times 15.3\);

\(30.6 \times PB = (15.3 + 11.9) \times 15.3\);

\(30.6 \times PB = 27.2 \times 15.3\);

PB = 416.16/30.6 = 13.6 cm;

Diameter (AB) = PA - PB = 30.6 - 13.6 = 17 cm;

Radius = AB/2 = 17/2 = 8.5 cm

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