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Circles Questions

Practice 31 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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31
Total Questions
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0
Easy
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26
Medium
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5
Hard
Practice by Exam:Mathematics(22)Quantitative Aptitude(9)

About Circles — practice questions, PYQs & concepts

Circles is a frequently-tested topic on Mathematics, Quantitative Aptitude. ExamTest.live currently lists 31 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 Mathematics (22) and Quantitative Aptitude (9). Click any exam chip above to drill down to that exam-specific question set.

How to use this page

  • Start easy: 0 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(1–31 of 31)

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Q1hardmcqMathematicsAIEEE 20042026
0% accuracy
If the lines and lie along diameters of a circle of circumference then the equation of the circle is
Q2hardmcqMathematicsAIEEE 20042026
0% accuracy
The intercept on the line by the circle is Equation of the circle on as a diameter is
Q3mediummcqQuantitative 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 )
Q4mediummcqQuantitative AptitudePrepp2026
0% accuracy
Tangents and are drawn from an external point to a circle with center . If , then find .
Q5mediummcqMathematicsAIEEE 20062026
0% accuracy
If the lines and are two diameters of a circle of area square units, the equation of the circle is:
Q6mediummcqMathematicsAIEEE 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:
Q7mediummcqMathematicsAIEEE 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:
Q8mediummcqMathematicsAIEEE 20072026
0% accuracy
The differential equation of all circles passing through the origin and having their centres on the -axis is:
Q9mediummcqMathematicsFIITJEE AIEEE 2011 (Set Q)2026
The two circles and () touch each other if:
Q10mediummcqMathematicsAIEEE2026
The differential equation of the family of circles with fixed radius units and centre on the line is:
Q11mediummcqMathematicsJEE Main2026
The circle passing through and touching the axis of at also passes through the point:
Q12mediummcqMathematicsJEE Main2026
The equation of the circle passing through the foci of the ellipse , and having centre at is:
Q13mediummcqQuantitative 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 )
Q14mediummcqQuantitative AptitudePrepp2026
From an external point , tangents and are drawn to a circle with centre . If , then find .
Q15mediummcqQuantitative 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 ).
Q16mediummcqQuantitative AptitudePrepp2026
Find the area of a minor sector of a circle whose circumference is and the length of its minor arc is (use ).
Q17mediummcqQuantitative AptitudePractice Test2026
Two circles of radii and are externally tangent to each other. Find the distance between their centres.
Q18mediummcqQuantitative 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:
Q19mediummcqQuantitative 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.
Q20mediummcqMathematicsAIEEE2026
The circle intersects the line at two distinct points if:
Q21mediummcqMathematicsAIEEE 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:
Q22mediummcqMathematicsAIEEE 20092026
If and are the points of intersection of the circles and , then there is a circle passing through and for:
Q23mediummcqMathematicsAIEEE2026
If the circles and intersect in two distinct points and , then the line passes through and for:
Q24mediummcqMathematicsAIEEE2026
The point diametrically opposite to the point on the circle is:
Q25mediummcqMathematicsAIEEE-CBSE-ENG-032026
The lines and are diameters of a circle having area as 154 sq units. Then the equation of the circle is:
Q26mediummcqMathematicsAIEEE-CBSE-ENG-032026
If the two circles and intersect in two distinct points, then:
Q27mediummcqMathematicsAIEEE2026
The plane cuts the sphere in a circle of radius:
Q28mediummcqMathematicsAIEEE2026
If a circle passes through the point and cuts the circle orthogonally, then the equation of the locus of its centre is:
Q29hardmcqMathematicsAIEEE 20042004
0% accuracy
If a circle passes through the point and cuts the circle orthogonally, then the locus of its centre is
Q30hardmcqMathematicsAIEEE 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
Q31hardmcqMathematicsAIEEE 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 31 Circles questions spread across 1 pages, covering easy, medium, and hard difficulty levels with detailed explanations.
Are Circles MCQs free?▼
Yes. All Circles questions, answers, and explanations on ExamTest.live are completely free. No account or subscription required.
Which exams include Circles questions?▼
Circles questions are commonly asked in Mathematics, Quantitative Aptitude. 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.