Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202616 April 2026Evening ShiftMathematicsCircleActual

Line l : x + y = 4 intersects the circle x^2 + y^2 - 2x - 2y = 2 at points A and B . If C is the center of the circle, then the area of ABC is...

Options

  1. A2
  2. B2
  3. C2 2
  4. D4

Correct answer

B. 2

Step-by-step solution

Equation of the circle is x^2 + y^2 - 2x - 2y = 2 , which can be written as (x-1)^2 + (y-1)^2 = 4 . Center of the circle is C(1, 1) and radius is R = 2 . The perpendicular distance d from the center C(1, 1) to the line x + y - 4 = 0 is given by d = |1 + 1 - 4| 1^2 + 1^2 = 2 . The length of the chord AB is 2 R^2 - d^2 = 2 2^2 - ( 2 )^2 = 2 2 . The area of ABC is 1 2 AB d = 1 2 2 2 2 = 2 . Answer: 2

Practice Circle on Quantrex Academy →

More from Circle

A circle touches both the coordinate axes and the straight line L 4 x +3 y -6=0 in the first quadrant. If this circle lies below the line L =0 , then the equation of that circle is 2025If the smallest circle through the points of intersection of x^2+y^2=a^2 and x +y =p, 0 < p < a is x^2+y^2-a^2+ (x +y -p)=0 then = 2025If the lines 3 x-4 y+4=0 and 6 x-8 y-7=0 are the tangents to the same circle, then the area of that circle (in sq.units) is 2025Circles are drawn through the point (2,0) to cut intercepts of length 5 units on the X -axis. If their centre lie in the first quadrant, then their equation is 2025The circles x^2+y^2-2 x-4 y-4=0 and x^2+y^2+2 x+4 y-11=0 2025If the line 4 x-3 y+7=0 touches the circle x^2+y^2-6 x+4 y-12=0 at ( , ) , then +2 = 2025The slope of the common tangent drawn to the circles x^2+y^2-4 x+12 y-216=0 and x^2+y^2+6 x-12 y+36=0 is 2025If r₁ and r₂ are radii of two circles touching all the four circles (x r)^2+(y r)^2=r^2 , then r₁+r₂ r = 2025 Full Circle list All MHT CET PYQs