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Mathematics - Circle

Practise 497 AP EAMCET previous year questions on Circle, compiled from papers spanning 2001 to 2025. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty AP EAMCET tests.

Circle has been asked in 24 of the 24 years of AP EAMCET papers analysed (2001–2024), with 497 questions in all. 33% of them were easy, 55% moderate and 12% tough. Most of its questions came from 2021, with 60 questions that year. In the last three years (2022–2024) it had 146 questions across 28 papers, about 5.2 per paper.

The chapter's 17 topics are not weighted equally: Equation of Circle & its intercept (105 questions, 21%), Tangent to circle (64 questions, 13%), and Intersection of Circles (57 questions, 11%) have been asked the most. Equation of Circle & its intercept has also led over the last five years, with 58 questions. Tangent to circle has produced the most tough questions (11).

  1. 1A circle touches both the coordinate axes and the straight line in the first quadrant. If this circle lies below the line , then the equatio27 May, 2025 (M)Tangent to circle
  2. 2If the smallest circle through the points of intersection of and is then27 May, 2025 (M)Family of Circle
  3. 3If the lines and are the tangents to the same circle, then the area of that circle (in sq.units) is27 May, 2025 (M)Tangent to circle
  4. 4Circles are drawn through the point to cut intercepts of length 5 units on the X -axis. If their centre lie in the first quadrant, then thei27 May, 2025 (M)Circle
  5. 5The circles and26 May, 2025 (M)Circle
  6. 6If the line touches the circle at , then26 May, 2025 (M)line and circle
  7. 7The slope of the common tangent drawn to the circles and is26 May, 2025 (M)Common Tangents
  8. 8If and are radii of two circles touching all the four circles , then26 May, 2025 (M)Equation of Circle & its intercept
  9. 9If the equation of the circle having the common chord to the circles and as its diameter is , then26 May, 2025 (M)Common Chord
  10. 10A circle passing through origin cuts the coordinate axes is and . If the straight line passes through a fixed point , then the locus of the 26 May, 2025 (E)Equation of Circle & its intercept
  11. 11If is the external centre of similitude of the circles and , then26 May, 2025 (E)Common Tangents
  12. 12The equation of the circle touching the lines is26 May, 2025 (E)Circle
  13. 13If the chord joining the points and on a circle subtends an angle of at any point on its circumference then the equation of such a circle is26 May, 2025 (E)Circle
  14. 14The equation of the circle which cuts all the three circles and orthogonally is26 May, 2025 (E)Circle
  15. 15If the equation of the circle passing through the point and having the lines and as its diameters is , then24 May, 2025 (M)Circle
  16. 16If is the equation of the polar of a point with respect to the circle , then24 May, 2025 (M)Chord of Contact
  17. 17If a unit circle touches the circle externally at the point , then24 May, 2025 (M)line and circle
  18. 18is a tangent to the circle at a point P. If C is the centre of the circle and Q is a point which divides CP in the ratio , then the power of24 May, 2025 (M)line and circle
  19. 19If the radical axis of the circles and touches the circle , then24 May, 2025 (M)Radical axis and centre
  20. 20Let and be two points. If P is a point in the coordinate plane such that , then the point P lies on the curve23 May, 2025 (M)Locus
  21. 21From a point , two tangents are drawn to the circle touching the circle at and . If the equation of the circle passing through and is , then23 May, 2025 (M)Tangent to circle
  22. 22If the equation of the polar of the point with respect to the circle is , then23 May, 2025 (M)Pole and Polar
  23. 23If is the angle between the tangents drawn from the point to the circle and , then the radius of the circle is23 May, 2025 (M)Tangent to circle
  24. 24If the power of the point with respect to the circle is -16, then23 May, 2025 (M)Circle
  25. 25The radius of the circle passing through the points of intersection of the circles and intersecting the circle orthogonally is23 May, 2025 (M)Circle
  26. 26P and Q are the ends of a diameter of the circle and are the lengths of the perpendiculars drawn from and onto the line respectively. When t23 May, 2025 (M)Equation of Circle & its intercept
  27. 27After the coordinate axes are rotated through an angle in the anti clockwise direction without shifting the origin, if the equation transfor23 May, 2025 (E)General Equation of 2nd degree curve
  28. 28If the circles and intersect at points and , then the line passes through and for23 May, 2025 (E)Common Chord
  29. 29The slope of one of the direct common tangents drawn to the circles and is23 May, 2025 (E)Common Tangents
  30. 30If are conjugate points with respect to the circle , then23 May, 2025 (E)Pole and Polar
  31. 31If the pole of the line with respect to the circle lies on the line , then the polar of the point with respect to the circle is23 May, 2025 (E)Pole and Polar
  32. 32If is the radical centre of the circles , and , then the length of the tangent drawn from to is23 May, 2025 (E)Radical axis and centre
  33. 33If is the inverse point of with respect to the circle , then the line containing is22 May, 2025 (M)Chord of Contact
  34. 34If the circle passing through and cuts the circle orthogonally, then22 May, 2025 (M)Intersection of Circles
  35. 35Length of the common chord of two circles of same radius is . If one of the two circles is , then acute angle between the two circles is22 May, 2025 (M)Circle
  36. 36A circle intersects another circle of radius 5 units such that their common chord is of maximum length. If the slope of that chord is , then22 May, 2025 (M)Circle
  37. 37Let be the angle between the circles and . If is an integer and then the radius of the circle is22 May, 2025 (M)Circle
  38. 38A circle passing through the point makes an intercept of length 4 units on X -axis and an intercept of length units on Y - axis. If the cent22 May, 2025 (E)Circle
  39. 39If is the inverse point of a point with respect to the circle then22 May, 2025 (E)Equation of Circle & its intercept
  40. 40If the equation of the circle lying in the first quadrant, touching both the coordinate axes and the line is , then22 May, 2025 (E)Circle
  41. 41If the point of contact of the circles and is , then22 May, 2025 (E)Circle
  42. 42If the circles and are orthogonal, then22 May, 2025 (E)Circle
  43. 43From a point P on the circle , two tangents are drawn to the circle . If and are the points of contact of those lines, then the locus of the21 May, 2025 (M)Locus
  44. 44If the product of the lengths of the perpendicular drawn from the ends of a diameter of the circle on to the line is maximum, then the two e21 May, 2025 (M)line and circle
  45. 45If the intercepts made by a variable circle on the X -axis and Y -axis are 8 and 6 units respectively, then the locus of the centre of the c21 May, 2025 (M)Equation of Circle & its intercept
  46. 46The slope of the non-vertical tangent drawn from the point to the circle is21 May, 2025 (M)Tangent to circle
  47. 47If the acute angle between the circles and is and the centre of lies in the first quadrant, then the radical axis of and is21 May, 2025 (M)Intersection of Circles
  48. 48If a circle passes through the origin and makes an intercept of length 4 units on the line , then the equation of the curve on which the cen21 May, 2025 (E)Equation of Circle & its intercept
  49. 49A circle touches the line at and passes through the point . Then a point that lies on the circle is21 May, 2025 (E)Family of Circle
  50. 50If is the common point for the circles and , then21 May, 2025 (E)Intersection of Circles

Frequently Asked Questions

1.How many questions are available for Circle?

This chapter includes 497 questions compiled from AP EAMCET papers spanning 2001 to 2025.

2.Are these questions only from AP EAMCET, or from other exams too?

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

3.Is Circle an important chapter for AP EAMCET Mathematics?

Circle has appeared in 25 of the 25 years of AP EAMCET papers covered here, with 497 questions across 93 papers - about 5 per paper it appears in.

4.What is the difficulty level of Circle questions in AP EAMCET?

Of the 497 questions analysed for this chapter, 33% are easy, 55% moderate and 12% tough. 2021 had the most, with 60 questions.

5.Which topics in Circle should I focus on?

These topics have carried the most weightage in Circle:

  • Equation of Circle & its intercept - 105 questions (21%)
  • Tangent to circle - 64 questions (13%)
  • Intersection of Circles - 57 questions (11%)
  • Tangent to circle has produced the most tough questions (11).
6.Is Circle's weightage in AP EAMCET going up or down?

Across all 93 papers analysed, Circle has averaged about 5.3 questions per paper. In the last three years (2022–2024), that average has stayed about the same, at about 5.2 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.