Ques. 1JEE Main 2025, 29 January (Morning Shift)
Let the line x + y = 1 meet the circle x2 + y2 = 4 at the points A and B. If the line perpendicular to AB and passing through the mid-point of the chord AB intersects the circle at C and D, then the area of the quadrilateral ABCD is equal to :
- 14
- 3 7
- 2 14
- 5 7
Answer
(3) 2 14
Solution
the perpendicular from the centre bisects a chord, the line through the mid-point of AB perpendicular to AB passes through the centre O(0, 0).
So CD is a diameter, CD = 2r = 4, and CD AB.
The distance of O from x + y = 1 is p = 1 2, so
AB = 2 r2 - p2 = 2 4 - 12 = 2 72 = 14
AB and CD are the perpendicular diagonals of the quadrilateral with vertices A, C, B, D.
Area = 12 AB CD = 12 14 4 = 2 14
Answer: (3)