CAT Circles Questions

Circle questions use relationships among radii, chords, tangents and angles. A well-labelled diagram often reveals a right triangle or an angle relationship that simplifies the problem.

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Key concepts

• Chord and central-angle relationships
• Tangents and radii
• Arcs, sectors and cyclic quadrilaterals

CAT circles practice questions

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Common mistakes

• Assuming an unmarked line passes through the centre.
• Confusing a sector's area with a segment's area.

Practical solving approaches

• Draw radii to contact points and relevant chord endpoints.
• Identify equal angles and right triangles before calculating lengths or areas.

Circles FAQs

What is the angle between a radius and a tangent?

At the point of contact, the radius is perpendicular to the tangent.

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CAT Circles Questions

Circle questions use relationships among radii, chords, tangents and angles. A well-labelled diagram often reveals a right triangle or an angle relationship that simplifies the problem.

15 free practice questions

Key concepts

• Chord and central-angle relationships
• Tangents and radii
• Arcs, sectors and cyclic quadrilaterals

CAT circles practice questions

Question 1Multiple choiceEASY

Question 1

Select the correct alternative from the given choices.

Answer the questions independently of each other.

What is the distance in cm between two parallel chords of lengths 32 cm and 24 cm in a circle of radius 20 cm?

 

Choose an answer

A.1 or 7B.2 or 14C.3 or 21
D.4 or 28

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Question 2Type in the answerMEDIUM

Question 2

Type in your answer in the input box provided below the question.

Answer the questions independently of each other.

Two chords of length 12 cm and 16 cm, of a circle of radius 10 cm, are perpendicular to each other. Find the distance between the midpoints of these two chords.

Your answer

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Question 3Multiple choiceMEDIUM

Question 3

Select the correct alternative from the given choices.

Answer the questions independently of each other.

A chord of length 32 cm is drawn inside a circle of radius 20 cm and a point, whose distance from the centre of the circle is 13 cm, is marked on the chord. Calculate the lengths of the segments of the chord made by this point.

Choose an answer

A.21 cm and 11 cmB.19 cm and 13 cmC.16 cm eachD.18 cm and 14 cm

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Question 4Multiple choiceMEDIUM

Question 4

Select the correct alternative from the given choices.

Answer the questions independently of each other.

On a trial track, a car starts from one end of the diameter of a semi-circular track. The radius of semi-circle is 14 m. The two front wheels of the car are 2 m apart. The car goes round the semi-circle and comes back to the starting point. Find out approximately, how many more metres does the outer wheel cover as compared to the inner wheel for one complete round, if the inner wheel is moving along the periphery of the semi-circular track?

Choose an answer

A.6.16 mB.30.54 mC.26.5 mD.12.57 m

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Question 5Multiple choiceMEDIUM

Question 5

Select the correct alternative from the given choices.

Answer the questions independently of each other.

Two circles with radii 3 units and 8 units touch each other externally. Three common tangents are drawn to these two circles. Find the area of the triangle enclosed by these three tangents.

Choose an answer

A.

B.

C.

D.

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Question 6Multiple choiceMEDIUM

Question 6

Select the correct alternative from the given choices.

Answer the questions independently of each other.

Three lines cross each other in a circle of radius 12 cm dividing the circle into maximum number of parts. What will be the approximate difference between the area of the largest possible triangle formed and the smallest possible area?

Choose an answer

A.

B.

C.

D.

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Question 7Multiple choiceMEDIUM

Question 7

Select the correct alternative from the given choices.

Answer the questions independently of each other.

Two identical circles intersect so that their centres, and the points at which they intersect, form a square of side 1 cm. The area in sq. cm of the portion that is common to the two circles is

Choose an answer

A.

B.

C.

D.0

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Question 8Multiple choiceMEDIUM

Question 8

Select the correct alternative from the given choices.

Answer the questions independently of each other.

A semi-circle is drawn with AB as its diameter. From C, a point on AB, a line perpendicular to AB is drawn meeting the circumference of the semi-circle at D. Given that AC = 2 cm and CD = 6 cm, the area ofthe semi-circle (in sq.cm) will be:

Choose an answer

A.

B.

C.

D.

E.

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Question 9Multiple choiceMEDIUM

Question 9

Select the correct alternative from the given choices.

A circle of radius 2 cm touches another circle of radius 10 cm internally. Find the length of a tangent segment drawn from the centre of the larger circle to the smaller circle.

Choose an answer

A.15 root 2 cmB.2 root 15 cmC.2 root 15 cmD.3root 15 cm

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Question 10Type in the answerMEDIUM

Question 10

Enter your response (as an integer) using the virtual keyboard in the box provided.

Your answer

Check answerView solution

Question 11Type in the answerMEDIUM

Question 11

Enter your response (as an integer) using the virtual keyboard in the box provided.

Your answer

Check answerView solution

Question 12Multiple choiceMEDIUM

Question 12

Select the correct alternative from the given choices

Choose an answer

A.1 : 2B.1 : 3C.1 : √3D.√3 : 2

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Question 13Multiple choiceMEDIUM

Question 13

Select the correct alternative from the given choices

Choose an answer

A.10√2 cmB.10 cmC.15/2 √2 cmD.15√2 cm

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Question 14Type in the answerMEDIUM

Question 14

Enter your response (as an integer) using the virtual keyboard in the box provided

Your answer

Check answerView solution

Question 15Multiple choiceEASY

Question 15

Select the correct alternative from the given choices

A circle is inscribed in ∆ XYZ, touching XY at P; XY = 7 units, YZ = 6 units, ZX = 8 units. Find XP.

Choose an answer

A.

B.

C.

D.

Check answerView solution

Common mistakes

• Assuming an unmarked line passes through the centre.
• Confusing a sector's area with a segment's area.

Practical solving approaches

• Draw radii to contact points and relevant chord endpoints.
• Identify equal angles and right triangles before calculating lengths or areas.

Circles FAQs

What is the angle between a radius and a tangent?

At the point of contact, the radius is perpendicular to the tangent.

More Geometry practice

• Coordinate geometry →
• Lines, angles & triangles →
• Mensuration (3D solids) →
• Quadrilaterals & polygons →