SSC CGL Geometry Tangent To Circle Set 2

SSC CGL Geometry Tangent To Circle Set 2 : Ques No 1

The radii of two non-intersecting circles are r₁ and r₂ with r₁ being the larger one and the smaller circle inscribed within the larger circle. if the least distance between their circumference be S, the distance between their centres is   

Options:

A. r₁ – r₂ + S

B. r₁ – r₂

C. r₁ + r₂ – S

D. r₁ – r₂ – S

Answer: D

Solution:

SSC CGL Geometry Tangent To Circle Set 2 : Ques No 2

CD is a common tangent to two circles with intersect each other at points A and B. Then, ∠CAD + ∠CBD is  

Options:

A. 120 degrees

B. 360 degrees

C. 90 degrees

D. 180 degrees

Answer: D

Solution:

SSC CGL Geometry Tangent To Circle Set 2 : Ques No 3

In the figure below, two lines RP and SP touch a circle with center  at O at points A and B respectively and meet at point P. If the line CD also touches the circle at point Q, then which of the following is correct?

Options:

A. BP = DP + PC + CD

B. 3BP = DP + PC + CD

C. 4BP = DP + PC + CD

D. 2BP = DP + PC + CD

Answer: D

Solution:

SSC CGL Geometry Tangent To Circle Set 2 : Ques No 4

In the figure below, ABRD is a quarter circle of radius 1 cm and a second circle is inscribed within the quarter circle touching it at three points. The radius of the inscribed circle (in cm) is

Options:

A. 1 – 2√2

B. (√2 + 1)/2

C. (√2 – 1)/2

D. (√2 – 1)

Answer: D

Solution:

SSC CGL Geometry Tangent To Circle Set 2 : Ques No 5

TP is the common tangent to two circles, the smaller with centre at O₁ touching the larger circle it with centre at O₂ at point P. The smaller circle is inside the larger one. If TQ is a second tangent to the larger circle at Q and TR is a second tangent to the smaller circle at R, then the ratio of TQ:TR is

Options:

A. 8 : 7

B. 7 : 8

C. 1 : 1

D. 5 : 4

Answer: C

Solution:

SSC CGL Geometry Tangent To Circle Set 2 : Ques No 6

In the figure below, two circles with centres at P and Q and each of radius 1 cm touch each other at O which is the centre of third circle of radius 2 cm. The fourth circle with centre at R touches all the three circles. The radius of the smallest fourth circle (in cm) is

Options:

A. 5

B. 2/3

C. 3/5

D. 3/7

Answer: B

Solution:

SSC CGL Geometry Tangent To Circle Set 2 : Ques No 7

The distance between the centres of two circles having radii 8 cm and 3 cm is 13 cm. The length (in cm) of the direct common tangent of the two circles is

Options:

A. 15

B. 12

C. 16

D. 18

Answer: B

Solution:

SSC CGL Geometry Tangent To Circle Set 2 : Ques No 8

AB is the diameter of a circle with centre at O. The tangent at C meets AB produced at Q. If ∠CAB = 34 degrees, then the value of ∠CBA is

Options:

A. 34 degrees

B. 56 degrees

C. 124 degrees

D. 68 degrees

Answer: B

Solution:

SSC CGL Geometry Tangent To Circle Set 2 : Ques No 9

Two circles touch each other externally at A. PQ is a direct common tangent to the two circles with P and Q as points as points of contact. If ∠APQ = 35 degrees, then ∠PQA is

Options:

A. 75 degrees

B. 65 degrees

C. 35 degrees

D. 55 degrees

Answer: D

Solution:

SSC CGL Geometry Tangent To Circle Set 2 : Ques No 10

Three circles of radius 6 cm each touch one another externally. Then the shortest distance from the centre of one circle to the line joining the centres of the other two circles is equal to

Options:

A. 6√7 cm

B. 6√2 cm

C. 6√5 cm

D. 6√3 cm

Answer: D

Solution: