JEE Main · Maths · Conic Sections
Circle Tangents: JEE Main previous year questions
62 questions in the 108 JEE Main shifts Lumi analysed, in 7 of 8 years. Pattern: Asked most years. 12 came in 2024–26. Here is how it is asked and which ideas come back.
- Questions
- 62
- in 52 of 108 shifts
- Years asked
- 7/8
- last asked 2026
- Weighted estimate
- 0.3
- model; history: 0.4 a shift on average, typically 0.1–0.6
Key findings
- 01
Asked in 7 of 8 years with analysed shifts and in 52 of 108 shifts: 62 questions, #35 of 196 topics.
- 02
44% of its questions since 2020 tested an idea no earlier year had asked; 26 repeated an idea from the year before.
- 03
The most repeated idea is Condition of tangency, asked 11 times in 11 shifts (2020, 2021, 2022, 2024), most often as “tangent point from circle centre and line”.
- 04
JEE Main has asked 19 of the 60 ideas in this topic; 36 have never been asked, directly or inside another question.
- 05
Mostly asked as single correct (60%); 40% need a numerical answer, 5% are easy and 39% hard. It went down from 0.5 to 0.3 questions a shift since 2024.
- 06
The skill tested most is multi-step (90%), then calculation (5%).
Questions a shift, year by year
Out of the 25 Maths questions in a shift. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift.
Raw count: 2017: 0 in 1 shift · 2020: 7 in 12 shifts · 2021: 19 in 24 shifts · 2022: 17 in 24 shifts · 2023: 7 in 12 shifts · 2024: 9 in 18 shifts · 2025: 2 in 8 shifts · 2026: 1 in 9 shifts.
- Up to 2023
- 0.5
- a shift, of 25
- Since 2024
- 0.3
- -0.2
- Usual gap
- 1.0 yrs
- between years asking it
- Shifts with it
- 52/108
- 48% of analysed shifts
How it is asked
Difficulty, format and skill
Across all 62 questions on Circle Tangents since 2017.
Difficulty
QUESTIONS- Easy3 · 5%
- Medium35 · 56%
- Hard24 · 39%
Format
SHARE- Single correct · 37 Q60%
- Numerical value · 25 Q40%
Skill tested
SHARE- Multi-step · 56 Q90%
- Calculation · 3 Q5%
- Application · 2 Q3%
- Conceptual · 1 Q2%
Repeats
New idea, or one asked before?
Each column is a year. Blue questions tested an idea no earlier year had asked; navy ones went back to an idea from an earlier year. 2017 is the first year, so everything in it counts as new. Heights are question counts, and Lumi analysed 1 to 24 shifts a year, so compare the split inside a column rather than heights across years.
- Idea asked for the first time
- Idea asked in an earlier year
Coverage of the topic
JEE Main has asked 19 of the 60 ideas in this topic. 36 have never been asked yet.
- Asked directly19 · 32%
- Touched inside another question5 · 8%
- Never asked36 · 60%
Ideas come from Lumi’s JEE syllabus map. A never-asked idea is not a safe skip: across all of JEE Main, 22% of questions since 2024 tested an idea no earlier year had asked.
Drill down
Chapter, idea, question
Every idea JEE Main tested in this topic, with its eight years. Open one to read the questions.
19 ideas inside
Squares are the 8 years with analysed shifts, 2017 to 2026. A number is the questions that year when there is more than one; the shade is scaled to one shift, so a year with more analysed shifts (1 to 24 a year) does not look darker. Share is of the level above.
Ideas
Every idea inside this topic
19 different ideas were tested; 8 came more than once.
tangent point from circle centre and line
Single correct · 11 shifts · 5 numericalcircle touching parabola at given point
Numerical value · 9 shifts · 6 numericalchord length of circle cut by line
Single correct · 8 shifts · 3 numericalrelative position of two circles
Single correct · 5 shifts · 2 numericalcontact point of externally touching circles
Numerical value · 5 shifts · 3 numericalarea of triangle from tangents to a circle
Single correct · 5 shifts · 1 numericalcircle from tangents and normal
Single correct · 4 shifts · 1 numericalshortest distance from point to circle
Single correct · 3 shifts · 1 numericallength of chord cut by line on a derived locus
Single correct · 1 shiftarea of triangle from tangent points
Single correct · 1 shiftcircumcircle of triangle from tangent points
Single correct · 1 shiftpole of chord cut by line on diameter circle
Single correct · 1 shiftdistance of pole from chord of contact
Numerical value · 1 shift · 1 numericalparameter from mirror image of circle
Numerical value · 1 shift · 1 numericalratio of segments cut by tangent to circle
Single correct · 1 shiftcontact point of internally touching circles
Numerical value · 1 shift · 1 numericalcondition for distinct chords bisected by axis
Single correct · 1 shiftlength of chord from tangent to another conic
Single correct · 1 shiftdistance to tangent perpendicular to given line
Single correct · 1 shift
| Idea | Years asked | Times | Shifts | Format | Numerical |
|---|---|---|---|---|---|
| Condition of tangencytangent point from circle centre and line | 11 | 11 | Single correctMulti-step | 5 | |
| Common Tangent to Circle and Coniccircle touching parabola at given point | 9 | 9 | Numerical valueMulti-step | 6 | |
| Family of Circles Touching a Linechord length of circle cut by line | 8 | 8 | Single correctMulti-step | 3 | |
| Number of Common Tangentsrelative position of two circles | 6 | 5 | Single correctApplication | 2 | |
| Common Tangent of Touching Circlescontact point of externally touching circles | 5 | 5 | Numerical valueMulti-step | 3 | |
| Area of Tangent-Chord Trianglearea of triangle from tangents to a circle | 5 | 5 | Single correctMulti-step | 1 | |
| Normal Passes Through Centercircle from tangents and normal | 4 | 4 | Single correctMulti-step | 1 | |
| Maximum and Minimum Distance to a Circleshortest distance from point to circle | 3 | 3 | Single correctMulti-step | 1 | |
| Locus of Midpoint of Chords of Contactlength of chord cut by line on a derived locus | 1 | 1 | Single correctMulti-step | – | |
| Area of Tangent-Chord Trianglearea of triangle from tangent points | 1 | 1 | Single correctMulti-step | – | |
| Circumcircle of Tangent Trianglecircumcircle of triangle from tangent points | 1 | 1 | Single correctMulti-step | – | |
| Equation of Polarpole of chord cut by line on diameter circle | 1 | 1 | Single correctMulti-step | – | |
| Chord of contactdistance of pole from chord of contact | 1 | 1 | Numerical valueMulti-step | 1 | |
| Reflection of Center Across Tangentparameter from mirror image of circle | 1 | 1 | Numerical valueMulti-step | 1 | |
| Tangent at a point (T=0)ratio of segments cut by tangent to circle | 1 | 1 | Single correctMulti-step | – | |
| Coordinates of Point of Contactcontact point of internally touching circles | 1 | 1 | Numerical valueMulti-step | 1 | |
| Equation of Chord with Given Midpoint (T = S1)condition for distinct chords bisected by axis | 1 | 1 | Single correctMulti-step | – | |
| Tangent in slope formlength of chord from tangent to another conic | 1 | 1 | Single correctMulti-step | – | |
| Tangent Parallel or Perpendicular to a Linedistance to tangent perpendicular to given line | 1 | 1 | Single correctMulti-step | – |
Times and shifts count every analysed shift. Across JEE Main, 78% of questions since 2024 went back to an idea an earlier year had asked; the rest were new. All repeated ideas
Every question
Circle Tangents questions, year by year
The newest 40 show their opening words as they appeared in the official paper; older ones name the idea they tested. Open one for its options and the official answer.
JEE Main 20261 question in 1 shift
- 6 Apr, Shift 2Q10Let C be a circle having centre in the first quadrant and touching the -axis at a distance of 3 units from the origin. If the circle C…
Idea: Family of Circles Touching a Line
Asked the year beforeMediumSingle correct
JEE Main 20252 questions in 2 shifts
- 2 Apr, Shift 1Q22The absolute difference between the squares of the radii of the two circles passing through the point and touching the lines…
Idea: Family of Circles Touching a Line
HardNumerical value - 7 Apr, Shift 1Q12Let be the circle in the third quadrant of radius 3, that touches both coordinate axes. Let be the circle with centre …
Idea: Common Tangent of Touching Circles
Asked the year beforeMediumSingle correct
JEE Main 20249 questions in 7 shifts
- 5 Apr, Shift 1Q13Let a circle C of radius 1 and closer to the origin be such that the lines passing through the point and parallel to the…
Idea: Maximum and Minimum Distance to a Circle
MediumSingle correct - 5 Apr, Shift 2Q14Let and be squares of side 4 and 2 units, respectively. The point is on the line segment and the point is on…
Idea: Condition of tangency
MediumSingle correct - 5 Apr, Shift 2Q24Let the maximum and minimum values of , be and , respectively. Then…
Idea: Maximum and Minimum Distance to a Circle
HardNumerical value - 8 Apr, Shift 1Q15Let the circles and touch each other externally at…
Idea: Common Tangent of Touching Circles
MediumSingle correct - 9 Apr, Shift 1Q29Let the centre of a circle, passing through the points , and touching the circle , be . Then for all…
Idea: Common Tangent of Touching Circles
HardNumerical value - 1 Feb, Shift 1Q15Let and be two circles. If the set of all values of so that the circles C and C'…
Idea: Number of Common Tangents
Asked the year beforeMediumSingle correct - 1 Feb, Shift 1Q29Let the line pass through the point of the intersection P (in the first quadrant) of the circle and the…
Idea: Condition of tangency
HardNumerical value - 1 Feb, Shift 2Q14Let the locus of the midpoints of the chords of the circle drawn from the origin intersect the line at and…
Idea: Locus of Midpoint of Chords of Contact
New ideaMediumSingle correct - 29 Jan, Shift 1Q27Equations of two diameters of a circle are and . The line joining the points and…
Idea: Condition of tangency
MediumNumerical value
JEE Main 20237 questions in 7 shifts
- 6 Apr, Shift 2Q13If the tangents at the points P and Q on the circle meet at the point , then the area of the…
Idea: Area of Tangent-Chord Triangle
New ideaMediumSingle correct - 8 Apr, Shift 2Q11Let be the origin and and be the tangents to the circle at the points and on it. If…
Idea: Circumcircle of Tangent Triangle
New ideaMediumSingle correct - 10 Apr, Shift 1Q29Let a common tangent to the curves and touch the curves at the points P and Q. Then is equal to…
Idea: Common Tangent to Circle and Conic
Asked the year beforeMediumNumerical value - 10 Apr, Shift 2Q13Let a circle of radius be concentric to the ellipse . Then the common tangents are inclined to the minor axis of…
Idea: Common Tangent to Circle and Conic
Asked the year beforeHardSingle correct - 13 Apr, Shift 1Q15Let the tangent and normal at the point on the ellipse meet the -axis at the points…
Idea: Equation of Polar
New ideaHardSingle correct - 13 Apr, Shift 2Q13Let the centre of a circle C be and its radius . Let and be two tangents and be a…
Idea: Normal Passes Through Center
Asked the year beforeMediumSingle correct - 15 Apr, Shift 1Q13The number of common tangents, to the circles and , is
Idea: Number of Common Tangents
EasySingle correct
JEE Main 202217 questions in 13 shifts
- 25 Jul, Shift 1Q29The sum of diameters of the circles that touch (i) the parabola at the point and…
Idea: Family of Circles Touching a Line
Asked the year beforeHardNumerical value - 25 Jul, Shift 2Q28If the circles and , touch…
Idea: Common Tangent of Touching Circles
Asked the year beforeMediumNumerical value - 27 Jul, Shift 2Q12A circle passes through the origin O and has diameter 4 on the positive -axis. The line gives a chord OA of circle…
Idea: Tangent at a point (T=0)
New ideaMediumSingle correct - 28 Jul, Shift 2Q73Let the tangents at two points A and B on the circle meet at origin O (0, 0). Then the area of the triangle OAB is :
Idea: Area of Tangent-Chord Triangle
Asked the year beforeMediumSingle correct - 28 Jul, Shift 2Q85Two tangent lines and are drawn from the point (2, 0) to the parabola . If the lines and are also tangent…
Idea: Common Tangent to Circle and Conic
Asked the year beforeHardNumerical value - 29 Jul, Shift 1Q8Let a line L pass through the point of intersection of the lines and ,…
Idea: Condition of tangency
Asked the year beforeHardSingle correct - 29 Jul, Shift 1Q30Let the mirror image of a circle in line be…
Idea: Reflection of Center Across Tangent
New ideaMediumNumerical value - 29 Jul, Shift 2Q28Let be a chord of length 12 of the circle . If tangents drawn to the circle at points and …
Idea: Chord of contact
New ideaMediumNumerical value - 24 Jun, Shift 1Q5Let be a circle passing through and touching the parabola at . Then is equal to ______.
Idea: Common Tangent to Circle and Conic
Asked the year beforeHardSingle correct - 24 Jun, Shift 2Q27Let a circle , , touch the -axis at . If the line intersects the circle at…
Idea: Family of Circles Touching a Line
Asked the year beforeMediumNumerical value - 25 Jun, Shift 1Q1Let a circle C touch the lines : and : , . If a line…
Idea: Family of Circles Touching a Line
Asked the year beforeMediumSingle correct - 25 Jun, Shift 1Q16If and , are two common tangents of circle and parabola , then the value of…
Idea: Common Tangent to Circle and Conic
Asked the year beforeHardSingle correct - 26 Jun, Shift 1Q23Let the common tangents to the curves and intersect at the point Q. Let an ellipse, centered at the origin…
Idea: Common Tangent to Circle and Conic
Asked the year beforeHardNumerical value - 28 Jun, Shift 1Q14If the tangents drawn at the points O(0, 0) and P on the circle intersect at the point Q,…
Idea: Area of Tangent-Chord Triangle
Asked the year beforeMediumSingle correct - 28 Jun, Shift 1Q30Let the lines and be normal to a circle . If the line…
Idea: Normal Passes Through Center
Asked the year beforeHardNumerical value - 29 Jun, Shift 1Q19Let the tangent to the circle at the point intersect the circle , at two…
Idea: Area of Tangent-Chord Triangle
Asked the year beforeHardSingle correct - 30 Jun, Shift 1Q14Consider three circles : If a line L :…
Idea: Condition of tangency
Asked the year beforeHardSingle correct
JEE Main 202119 questions in 15 shifts
- 3 Aug, Shift 2Q86The circles, and touch each other internally. If the point of contact of these…
Idea: Coordinates of Point of Contact
New ideaMediumNumerical value - 4 Aug, Shift 1Q73Consider a family of circles which pass through the point and touch the axis of . If the centre of such a circle is at…
Idea: Family of Circles Touching a Line
Asked the year beforeMediumSingle correct - 4 Aug, Shift 2Q72If two distinct chords, drawn from the point on the circle (where ) are…
Idea: Equation of Chord with Given Midpoint (T = S1)
New ideaHardSingle correct - 26 Aug, Shift 1Q73If a line along a chord of the circle , passes through the point and is tangent to the parabola…
Idea: Tangent in slope form
New ideaHardSingle correct - 26 Aug, Shift 2 · Q71Family of Circles Touching a LineAsked the year beforeHard
- 27 Aug, Shift 2 · Q85Common Tangent of Touching CirclesNew ideaMedium
- 31 Aug, Shift 1 · Q86Condition of tangencyAsked the year beforeHard
- 31 Aug, Shift 2 · Q88Area of Tangent-Chord TriangleNew ideaHard
- 31 Aug, Shift 2 · Q89Common Tangent to Circle and ConicNew ideaMedium
- 25 Feb, Shift 1 · Q62Normal Passes Through CenterNew ideaHard
- 25 Feb, Shift 2 · Q89Common Tangent to Circle and ConicNew ideaHard
- 26 Feb, Shift 2 · Q70Maximum and Minimum Distance to a CircleNew ideaMedium
- 26 Feb, Shift 2 · Q90Common Tangent to Circle and ConicNew ideaHard
- 16 Mar, Shift 2 · Q62Tangent Parallel or Perpendicular to a LineNew ideaMedium
- 17 Mar, Shift 1 · Q74Normal Passes Through CenterNew ideaMedium
- 17 Mar, Shift 1 · Q75Number of Common TangentsAsked the year beforeMedium
- 17 Mar, Shift 1 · Q86Number of Common TangentsAsked the year beforeEasy
- 17 Mar, Shift 2 · Q78Area of Tangent-Chord TriangleNew ideaMedium
- 18 Mar, Shift 1 · Q75Number of Common TangentsAsked the year beforeEasy
JEE Main 20207 questions in 7 shifts
- 8 Jan, Shift 2 · Q64Condition of tangencyNew ideaMedium
- 9 Jan, Shift 1 · Q65Condition of tangencyNew ideaMedium
- 9 Jan, Shift 2 · Q73Number of Common TangentsNew ideaMedium
- 2 Sep, Shift 1 · Q74Condition of tangencyNew ideaMedium
- 3 Sep, Shift 1 · Q75Condition of tangencyNew ideaMedium
- 5 Sep, Shift 1 · Q64Condition of tangencyNew ideaMedium
- 6 Sep, Shift 2 · Q65Family of Circles Touching a LineNew ideaHard
Questions from the official JEE Main Paper 1 shifts published by NTA (CBSE for 2017). Questions NTA dropped are left out. Topic and idea tags, counts and notes are Lumi’s.