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Friday, 9 October

JEE Main 2022 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 29 June 2022, Shift 1, Maths Q19

Question 19 of 90 in this shift, Maths question 19 of 30, Section A.

Let the tangent to the circle C1:x2+y2=2C_1: x^2 + y^2 = 2 at the point M(−1,1)M(-1, 1) intersect the circle C2:(x−3)2+(y−2)2=5C_2: (x - 3)^2 + (y - 2)^2 = 5, at two distinct points A and B. If the tangents to C2C_2 at the points A and B intersect at N, then the area of the triangle ANB is equal to :
  1. (1)12\frac{1}{2}
  2. (2)23\frac{2}{3}
  3. (3)16\frac{1}{6}Official answer
  4. (4)53\frac{5}{3}

Official answer

Option 3

NTA final key (2022 Session 1).

Chapter
Conic Sections
Topic
Circle Tangents
Idea tested
Area of Tangent-Chord Triangle

Same topic in other shifts

All Circle Tangents questions
  1. 6 Apr 2026, Shift 2 · Q10Let C be a circle having centre in the first quadrant and touching the xx-axis at a distance of 3 units from the origin. If the circle C…MediumSingle correct
  2. 2 Apr 2025, Shift 1 · Q22The absolute difference between the squares of the radii of the two circles passing through the point (−9,4)(-9, 4) and touching the lines…HardNumerical value
  3. 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
  4. 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
  5. 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
  6. 29 Jan 2024, Shift 1 · Q27Equations of two diameters of a circle are 2x−3y=52x-3y=5 and 3x−4y=73x-4y=7. The line joining the points (−227,−4)\left(-\frac{22}{7},-4\right) and…MediumNumerical value

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 42 of the 174 JEE Main shifts held from 2017 to 2026.