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CGP EDU Academic Team
Published on: August 13, 2026
If a, b, c are sides of triangle ABC, and (a + b – c) (b + c – a) = λ ac, then values of λ for which above equation holds is/are-
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(a, d)
Given a, b, c are the sides of the triangle.
(a + b – c) (b + c – a) = λ ac
⇒ 2ac – (a 2 + c 2 – b 2 ) = λ ac
∴ 2 ac – 2ac cos β = λ ac
2ac (1 – cos β ) = λ ac
⇒ 4ac sin2 β /2 = λ ac ⇒ sin –1 β = – 
0 ≤ 
≤ 1 = 0 < λ ≤ 4
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