JEE Main 2022 Mathematics question

Let the circumcentre of a triangle with vertices A(a, 3), B(b, 5) and C(a, b), ab > 0 be P(1, 1). If the line AP intersects the line BC at the point , ), then is equal to :

(1)2
(2)4/7Correct
(3)2/7
(4)4

Answer: (2)

Solution

AC is vertical (A and C have the same x-coordinate), so the perpendicular bisector of AC is the horizontal line y = (b + 3)/2, which passes through P(1, 1): b = −1. P is also equidistant from A and B:

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Question ID VK-035148