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Mathematics - Circle

Practise 105 NTA Abhyas (JEE Main) questions on Circle. Each question shows a quick preview so you can jump straight to the topic you want to revise.

Circle has been asked in 0 of the 24 years of NTA Abhyas (JEE Main) papers analysed (2002–2025), with 105 questions in all. 100% of them were easy, 0% moderate and 0% tough. Most of its questions came from 2025, with 0 questions that year. In the last three years (2023–2025) it had 0 questions across 63 papers, about 0 per paper.

All of the chapter's questions come from a single topic, Uncategorized.

  1. 1If the circles x - 3 2 + y - 4 4 = 16 and x - 7 2 + y - 7 2 = 9 intersect at points A and B , then the area (in sq. units) of the quadrilate
  2. 2A point P moves such that the chord of contact of P with respect to the circle x 2 + y 2 = 4 passes through the point 1 , 1 . The coordinate
  3. 3The perimeter of the locus of the point at which the two circles x 2 + y 2 = 1 and x - 4 2 + y 2 = 4 subtend equal angles is
  4. 4The number of rational point(s) (a point ( a , b ) is rational, if a and b both are rational numbers) on the circumference of a circle havin
  5. 5Let four circles having radii r 1 = 5 units , r 2 = 5 units , r 3 = 8 units and r 4 units r 4 5 are mutually touching each other externally,
  6. 6Let p and q be the length of two chords of a circle which subtend angles 3 6 o and 6 0 o respectively at the centre of the circle. Then, the
  7. 7Let two circles having radii r 1 and r 2 are orthogonal to each other. If the length of their common chord is k times the square root of har
  8. 8Let the lines y - 2 = m 1 x - 5 and y + 4 = m 2 x - 3 intersect at right angles at P (where m 1 and m 2 are parameters). If locus of P is x
  9. 9The centre of the circle passing through the points of intersection of the curves 2 x + 3 y + 4 3 x + 2 y - 1 = 0 and x y = 0 is
  10. 10The distance of the y -axis from the center of the circle which lies in the first quadrant (see figure) and tangent to the lines y = 1 2 x ,
  11. 11Let triangle A B C is right-angled at A . The circle with centre A and radius A B cuts B C and A C internally at D and E respectively. If B
  12. 12The two circles x 2 + y 2 = a x and x 2 + y 2 = c 2 c 0 touch each other, if c a is equal to
  13. 13The equation of an ex-circle of a triangle formed by the common tangents to the circle x 2 + y 2 = 4 and x 2 + y 2 - 6 x + 8 = 0 is
  14. 14Let C 1 and C 2 be two circles of radius r 1 and r 2 units respectively touching both the axes. If the two circles are orthogonal, then r 1
  15. 15Lines L 1 L 2 are rotating in an anticlockwise direction about the points A – 2 , 0 and B 2 , 0 respectively in such a way that the speed of
  16. 16Suppose the family of lines a x + b y + c = 0 (where a , b , c are in arithmetic progression) be normal to a family of circles. The radius o
  17. 17A straight line l 1 with equation x - 2 y + 10 = 0 meets the circle with equation x 2 + y 2 = 100 at B in the first quadrant. A line through
  18. 18Line L 1 ≡ 3 x - 4 y + 1 = 0 touches the circles C 1 and C 2 . Centres of C 1 and C 2 are A 1 1,2 and A 2 3,1 respectively, then identify th
  19. 19The possible number of values of a for which the common chord of the circles x 2 + y 2 = 8 and x - a 2 + y 2 = 8 subtends a right angle at t
  20. 20The length of the radius of the circle which touches the x -axis at the point 1 , 0 and passes through the point 2 , 3 is
  21. 21Let P Q be the common chord of the circles S 1 : x 2 + y 2 + 2 x + 3 y + 1 = 0 and S 2 : x 2 + y 2 + 4 x + 3 y + 2 = 0 , then the perimeter
  22. 22If the circles x 2 + y 2 - 10 x + 16 y + 89 - r 2 = 0 and x 2 + y 2 + 6 x - 14 y + 42 = 0 have common points, then the number of possible in
  23. 23Tangents are drawn to a unit circle with centre at the origin from each point on the line x + y = 2 . Then, the area (in sq. units) of the l
  24. 24Two circles have a direct common tangent with length 36 c m . The shortest distance between these circles is 14 c m . If the radius of the l
  25. 25Consider circles C 1 and C 2 touching both the axes and passing through 4 , 4 , then the x -intercept of the common chord of the circles is
  26. 26The equation of incircle of the triangle formed by common tangents to the circles x 2 + y 2 = 4 and x 2 + y 2 - 6 x + 8 = 0 is
  27. 27Let the lines 4 x - 3 y + 10 = 0 and 4 x - 3 y - 30 = 0 make equal intercepts of 6 units with a circle C whose centre lies on 2 x + y = 0 ,
  28. 28The lines joining the origin to the points of intersection of the line 4 x + 3 y = 24 with the circle x - 3 2 + y - 4 2 = 25 are
  29. 29The sum of the slopes of all possible chords of the circle x 2 + y 2 = 100 , which passes through 7 , 1 and also divide the circumference of
  30. 30The line 2 x - y + 1 = 0 is tangent to the circle at the point 2,5 and the centre of the circle lies on x - 2 y = 4 . The square of the radi
  31. 31Which of the following equations of a line intercepts on the circle x 2 + y 2 - 6 x - 8 y = 0 a chord of longest length?
  32. 32The tangent to the circle x 2 + y 2 = 5 at the point 1 , - 2 also touches the circle x 2 + y 2 - 8 x + 6 y + 20 = 0 at the point
  33. 33The least value of the quadratic polynomial, f x = 2 p 2 + 1 x 2 + 2 4 p 2 - 1 x + 4 2 p 2 + 1 for real values of p and x is
  34. 34Let circles C 1 , C 2 and C 3 with centres O 1 , O 2 and O 3 respectively touch each other externally, where O 1 = - 36,7 , O 2 = 20,7 and O
  35. 35The radius of the circle with centre at 3,2 and whose common chord with the circle C : x 2 + y 2 - 4 x - 8 y + 16 = 0 is also a diameter of
  36. 36Consider circles C 1 C 2 touching both the axes and passing through 4,4 , then the product of radii of these circles is
  37. 37The value of λ for which the set x , y : x 2 + y 2 - 6 x + 4 y ≤ 12 ∩ x , y : 4 x + 3 y ≤ λ contains only one point is
  38. 38The area (in sq. units) of the circle touching the line x + y = 4 at 1 , 3 and intersecting x 2 + y 2 = 4 orthogonally is equal to
  39. 39Let the points A : 0 , a , B : - 2,0 and C : 1 ,1 form an obtuse angled triangle (obtuse angled at angle A ), then the complete set of value
  40. 40A circle of radius 2 units is touching both the axes and a circle with centre at ( 6 , 5 ) . The distance between their centers is
  41. 41The centres of two circles C 1 and C 2 each of unit radius are at a distance of 6 units from each other. Let P be the midpoint of the line s
  42. 42If the length of direct common tangent and transverse common tangent of two circles with integral radii are 3 units and 1 unit respectively,
  43. 43The number of common tangents to the circles x 2 + y 2 + 2 x + 8 y - 23 = 0 and x 2 + y 2 - 4 x - 10 y + 9 = 0 , are
  44. 44From the point A 0 , 3 on the circle x 2 + 4 x + y - 3 2 = 0 , a chord A B is drawn and extended from point B to a point M such that A M = 2
  45. 45For a A B C the vertices are A 0,3 , B 0,12 and C x , 0 . If the circumcircle of A B C touches the x -axis, then the area (in sq. units) of
  46. 46If O is the origin and O P , O Q are distinct tangents to the circle x 2 + y 2 + 2 g x + 2 f y + c = 0 , then the circumcentre of the triang
  47. 47The equation of the circle whose radius is 5 units and which touches the circle x 2 + y 2 - 2 x - 4 y - 20 = 0 externally at the point 5,5 i
  48. 48In the figure P Q , P O 1 and O 1 Q are the diameters of semicircles C 1 , C 2 and C 3 with centres at O 1 , O 2 and O 3 respectively and th
  49. 49The tangents to x 2 + y 2 = a 2 having inclinations and intersect at P . If cot + cot = 0 , then the locus of P is
  50. 50From a point P 3,3 on the circle x 2 + y 2 = 18 two chords P Q and P R each of length 2 units are drawn on this circle. Then, the value of t

Frequently Asked Questions

1.How many questions are available for Circle?

This chapter includes 105 NTA Abhyas (JEE Main) questions.

2.Are these questions only from NTA Abhyas (JEE Main), or from other exams too?

These are NTA Abhyas (JEE Main) questions specifically for the Circle chapter. Questions from other exams like JEE Main or JEE Advanced are organised separately under their respective exam sections.

3.What is the difficulty level of Circle questions in NTA Abhyas (JEE Main)?

Of the 105 questions analysed for this chapter, 100% are easy, 0% moderate and 0% tough. 2025 had the most, with 0 questions.

4.Which topics in Circle should I focus on?

All of this chapter's questions come from a single topic: Uncategorized.