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Circles Questions

Practice 59 Circles questions with detailed answers and explanations. Free MCQs, PYQs, and mock test questions for NEET, JEE, GATE, SSC and more.

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59
Total Questions
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4
Easy
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50
Medium
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5
Hard
Practice by Exam:Quantitative Aptitude(31)Mathematics(26)Mathematics and Science(2)

About Circles — practice questions, PYQs & concepts

Circles is a frequently-tested topic on Quantitative Aptitude, Mathematics, Mathematics and Science. ExamTest.live currently lists 59 Circles questions spanning previous-year papers from 2004 to 2026, each with worked solutions and a step-by-step explanation. Use the filters on this page to focus on a specific exam, difficulty level or year — every answer key is free, no sign-up required.

Circles weight in competitive exams

Across our Circles question bank, the largest sources are Quantitative Aptitude (31), Mathematics (26) and Mathematics and Science (2). Click any exam chip above to drill down to that exam-specific question set.

How to use this page

  • Start easy: 4 easy Circles questions are available — build fluency before moving up.
  • Target weak years: Use the year filter to focus on the most recent 2026 paper or older PYQs you have not attempted.
  • Time yourself: Every question shows the average solve time so you can benchmark your speed against other students.
  • Read every explanation: Even on questions you got right — the explanation often surfaces a faster approach you can reuse.

All Circles Questions(1–59 of 59)

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Q1mediummcqQuantitative AptitudeCompetitive Exam2026
0% accuracy
A 70cm wide path is made around a circular garden having a diameter of 14 metres. What is the area of the path (in m
2
)?
Q2easymcqQuantitative AptitudeCompetitive Exam Practice2026
0% accuracy
The longest chord of a circle is equal to:
Q3mediummcqQuantitative AptitudeWest Bengal Civil Services2026
0% accuracy
A quadrant of a circle contains a shaded region formed by a circular arc and its bounding radii. What is the ratio of the perimeter of this shaded quadrant region to the total circumference of the original circle?

image
Q4mediummcqMathematicsCompetitive Exam2026
100% accuracy
The ratio of the radii of two circles is . What is the ratio of their areas?
Q5mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
A race track is in the shape of a ring whose inner and outer circumferences are 880 m and 1012 m, respectively. What is the area (in m
2
) of the track? (Take π=
7
22
​
)
Q6mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
What will be the value of the angle (in degrees) subtended by the chord in the minor segment of the circle, if the length of a chord is equal to the radius of the circle?
Q7hardmcqMathematicsAIEEE 20042026
0% accuracy
If the lines and lie along diameters of a circle of circumference then the equation of the circle is
Q8hardmcqMathematicsAIEEE 20042026
0% accuracy
The intercept on the line by the circle is Equation of the circle on as a diameter is
Q9mediummcqMathematicsAIEEE 20062026
0% accuracy
Let be the circle with centre and radius units. The equation of the locus of the mid points of the chords of the circle that subtend an angle of at its centre is:
Q10mediummcqMathematicsAIEEE 20062026
0% accuracy
If the lines and are two diameters of a circle of area square units, the equation of the circle is:
Q11mediummcqMathematicsAIEEE 20072026
0% accuracy
The differential equation of all circles passing through the origin and having their centres on the -axis is:
Q12mediummcqMathematicsAIEEE 20072026
0% accuracy
Consider a family of circles which are passing through the point and are tangent to the -axis. If are the coordinates of the centre of the circles, then the set of values of is given by the interval:
Q13mediummcqQuantitative AptitudePrepp2026
0% accuracy
Tangents and are drawn from an external point to a circle with center . If , then find .
Q14mediummcqQuantitative AptitudePrepp2026
0% accuracy
The length of a chord subtended by an arc of a circle is equal to the radius of the circle. If the radius of the circle is , then find the length of the arc (in units). (Take )
Q15mediummcqQuantitative AptitudeStaff Selection Commission2026
Calculate the length (in ) of , if the radius of the circle is and the line through the centre meets the tangent at point such that .

image
Q16mediummcqQuantitative AptitudeCompetitive Exam2026
In a circle touching the side of at and sides and produced at and respectively. If , then the perimeter of is:
Q17mediummcqQuantitative AptitudeSSC CGL2026
Find the measure of the central angle of the arc whose length is and the radius of the circle is .
Q18mediummcqQuantitative AptitudeCompetitive Exam2026
The area of a circle is . Find its radius (in ).
Q19mediummcqQuantitative AptitudeCompetitive Exam2026
The chord of a circle is in length and at a distance of from the centre. Calculate the angle subtended by the chord at the centre of the circle.
Q20mediummcqQuantitative AptitudeCompetitive Exam2026
The centres of two circles of radii 20cm and 32cm are 60cm apart. What is the ratio of the length of the direct common tangent to the length of the transverse common tangent to these circles?
Q21mediummcqQuantitative AptitudeSSC CGL2026
In a circle with centre 'O', if the angle subtended by an arc at the circumference ∠BCA=50
∘
, then what is the value of ∠BDA where D is another point on the same major arc segment?

image
Q22easymcqQuantitative AptitudeStaff Selection Commission2026
The circumference of a circle is . Find its radius (in ).
Q23mediummcqQuantitative AptitudeSSC CGL2026
Find the length of the arc whose central angle is 45
∘
and the radius of the circle is 28cm. (Take π=
7
22
​
)
Q24mediummcqQuantitative AptitudeCompetitive Exam2026
The length of a radius of a circle is and the length of a chord of the circle is , the distance of the chord from the center of the circle is
Q25mediummcqQuantitative AptitudeCompetitive Exam2026
If area of circular field is sq. unit, perimeter is unit and length of diameter is unit then the value of is
Q26mediummcqQuantitative AptitudeCompetitive Exam Practice2026
PQ is a diameter of a circle and PS is a chord. If PQ is 82cm and PS is 80cm, the distance (in cm) of PS from the center of the circle is:
Q27mediummcqQuantitative AptitudeCompetitive Exam2026
The lengths of two parallel chords of a circle are and . If the smaller chord is at a distance of from the centre, then the distance of the other chord from the centre is:
Q28mediummcqMathematicsCompetitive Exam2026
Two circles with radii and respectively, touch each other externally. Let be the radius of a circle that touches these two circles as well as their common tangent line. Which of the following relations is true?

image
Q29mediummcqQuantitative AptitudeCompetitive Exam2026
In a circle touching the side of at and sides and produced at and respectively. If , then the perimeter of is:

image
Q30mediummcqQuantitative AptitudeCompetitive Exam2026
If a shaded region is perfectly formed by a quadrant (one-fourth sector) of a circle, what is the ratio of the perimeter of this shaded region to the total circumference of the circle?

image
Q31mediummcqQuantitative AptitudeCompetitive Exam2026
The ratio of the radii of two circles is . What is the ratio of their respective areas?
Q32mediummcqQuantitative AptitudeWBCS Prelims2026
What is the ratio between area of circles circumscribing a square and that of the one inscribed in the square?
Q33mediummcqQuantitative AptitudeWBCS Prelims2026
The distance between the centres of two circles of radii and is . The length of direct tangent (in ) is
Q34mediummcqMathematicsCompetitive Exam2026
An arc of length subtends an angle of at the centre of a circle. The radius of the circle is:
Q35mediummcqMathematicsFIITJEE AIEEE 2011 (Set Q)2026
The two circles and () touch each other if:
Q36mediummcqMathematicsAIEEE2026
If the circles and intersect in two distinct points and , then the line passes through and for:
Q37mediummcqMathematicsAIEEE2026
If a circle passes through the point and cuts the circle orthogonally, then the equation of the locus of its centre is:
Q38mediummcqMathematicsAIEEE-CBSE-ENG-032026
If the two circles and intersect in two distinct points, then:
Q39mediummcqMathematicsAIEEE-CBSE-ENG-032026
The lines and are diameters of a circle having area as 154 sq units. Then the equation of the circle is:
Q40mediummcqMathematicsAIEEE2026
The differential equation of the family of circles with fixed radius units and centre on the line is:
Q41mediummcqMathematicsAIEEE2026
The point diametrically opposite to the point on the circle is:
Q42mediummcqMathematicsAIEEE 20092026
If and are the points of intersection of the circles and , then there is a circle passing through and for:
Q43mediummcqMathematicsAIEEE 20092026
Three distinct points and are given such that the ratio of the distance of any one of them from the point to the distance from the point is equal to . Then the circumcentre of the triangle is at the point:
Q44mediummcqMathematicsAIEEE2026
The circle intersects the line at two distinct points if:
Q45mediummcqMathematicsJEE Main2026
The circle passing through and touching the axis of at also passes through the point:
Q46mediummcqMathematicsJEE Main2026
The equation of the circle passing through the foci of the ellipse , and having centre at is:
Q47mediummcqQuantitative AptitudePrepp2026
The chord length of a chord made on an arc of a circle is equal to the radius of the circle. Find the length of the arc (in units), if the radius of the circle is 21 units. (Take )
Q48mediummcqQuantitative AptitudePrepp2026
From an external point , tangents and are drawn to a circle with centre . If , then find .
Q49mediummcqQuantitative AptitudePrepp2026
Find the area of a minor sector of a circle whose circumference is and the length of its minor arc is (use ).
Q50mediummcqQuantitative AptitudePrepp2026
Two circles with centers and have radii and , respectively. is tangent to both circles. If and intersect at the point , and , then find the value of (in ).
Q51mediummcqQuantitative AptitudePractice Test2026
Two circles of radii and are externally tangent to each other. Find the distance between their centres.
Q52mediummcqMathematicsAIEEE2026
The plane cuts the sphere in a circle of radius:
Q53mediummcqQuantitative AptitudeCompetitive Exam Practice2026
Find the area (in cm
2
) of a circle with a maximum radius that can be inscribed in a rectangle of length 18cm and breadth 12cm.
Q54easymcqMathematicsUPTET 2021 Memory Based Paper 12026
If the distance between the centres of two circles is less than the sum of radii of the two, then they:
Q55easymcqMathematics and ScienceUPTET Paper 2 (Maths & Science)2018
If the distance between center to chord is and the length of the chord is , then the diameter of the circle is
Q56mediummcqMathematics and ScienceUPTET Paper 2 (Maths & Science)2018
In the following figure, is a secant and is a tangent to the circle. If and , then find the measurement of .
Q57hardmcqMathematicsAIEEE 20042004
0% accuracy
A variable circle passes through the fixed point and touches -axis. The locus of the other end of the diameter through is
Q58hardmcqMathematicsAIEEE 20042004
0% accuracy
If a circle passes through the point and cuts the circle orthogonally, then the locus of its centre is
Q59hardmcqMathematicsAIEEE 20042004
0% accuracy
The normal to the curve at ' ' always passes through the fixed point

Frequently Asked Questions

How many Circles questions are on ExamTest.live?▼
We have 59 Circles questions spread across 1 pages, covering easy, medium, and hard difficulty levels with detailed explanations.
Are Circles MCQs free?▼
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Which exams include Circles questions?▼
Circles questions are commonly asked in Quantitative Aptitude, Mathematics, Mathematics and Science. You can filter by exam using the links above.
How do I practice Circles questions effectively?▼
Start with easy questions to build confidence, then tackle medium and hard ones. Use the filter buttons to sort by difficulty. Reveal the answer only after attempting each question, and read the explanation thoroughly.