JEE Main 2024 Mathematics question
Consider two circles C₁ : x² + y² = 25 and C₂ : (x − α)² + y² = 16, where α ∈ (5, 9). Let the angle between the two radii (one to each circle) drawn from one of the intersection points of C₁ and C₂ be sin⁻¹(√63/8). If the length of common chord of C₁ and C₂ is β, then the value of (αβ)² equals .
Answer: 1575
Solution
The triangle formed by the two centres and an intersection point P has sides 5, 4 and α, with the angle sinθ = √63/8
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