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Saturday, 31 October

JEE Main · Maths · Conic Sections

Common Tangent of Touching Circles

JEE Main asked Common Tangent of Touching Circles 5 times in 5 of the 108 shifts Lumi analysed, in 2021, 2022, 2024 and 2025. It belongs to Circle Tangents, in Conic Sections (Maths). The longest wait between two years asking it was 2 years. In 2024 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
5
in 5 shifts
Years
4 of 8
First asked
2021
last in 2025
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2021, 2022, 2024 and 2025. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.10.20’170’200.03’210.04’220’230.09’240.13’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 1 in 24 shifts · 2022: 1 in 24 shifts · 2023: 0 in 12 shifts · 2024: 2 in 18 shifts · 2025: 1 in 8 shifts · 2026: 0 in 9 shifts.

Shift by shift

Each square is one analysed shift, in date order. Open a filled one for that paper.

  • 20260 of 9
  • 20251 of 8
  • 20242 of 18
  • 20230 of 12
  • 20221 of 24
  • 20211 of 24
  • 20200 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Numerical value is the usual form. Skill tested: multi-step.

  • Contact point of externally touching circles
  • Circle parameters from touching condition

Difficulty

Easy 0Medium 4Hard 1

3 of the 5 questions had a numerical answer.

Every question

All 5 questions

From the official JEE Main shift papers, newest first. Open one for the full question, the options and the official answer.

  1. 7 Apr 2025, Shift 1 · Q12Let C1C_1 be the circle in the third quadrant of radius 3, that touches both coordinate axes. Let C2C_2 be the circle with centre (1,3)(1, 3)…MediumSingle correct
  2. 9 Apr 2024, Shift 1 · Q29Let the centre of a circle, passing through the points (0,0)(0,0), (1,0)(1,0) and touching the circle x2+y2=9x^2+y^2=9, be (h,k)(h,k). Then for all…HardNumerical value
  3. 8 Apr 2024, Shift 1 · Q15Let the circles C1:(x−α)2+(y−β)2=r12C_1:(x-\alpha)^2+(y-\beta)^2=r_1^2 and C2:(x−8)2+(y−152)2=r22C_2:(x-8)^2+\left(y-\frac{15}{2}\right)^2=r_2^2 touch each other externally at…MediumSingle correct
  4. 25 Jul 2022, Shift 2 · Q28If the circles x2+y2+6x+8y+16=0x^2+y^2+6x+8y+16=0 and x2+y2+2(3−3)x+2(4−6)y=k+63+86, k>0x^2+y^2+2\left(3-\sqrt{3}\right)x+2\left(4-\sqrt{6}\right)y=k+6\sqrt{3}+8\sqrt{6},\ k>0, touch…MediumNumerical value
  5. 27 Aug 2021, Shift 2 · Q85Two circles each of radius 5 units touch each other at the point (1,2)(1, 2). If the equation of their common tangent is 4x+3y=104x + 3y = 10, and…MediumNumerical value

Shifts: 27 Aug 2021, Shift 2, 25 Jul 2022, Shift 2, 8 Apr 2024, Shift 1, 9 Apr 2024, Shift 1, 7 Apr 2025, Shift 1.

Same topic

Other ideas in Circle Tangents

Circle Tangents has 19 ideas JEE Main has asked; 8 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas