Published by:
CGP EDU Academic Team
Published on: August 13, 2026
The line x + y = a meets the x-axis of A and y-axis at B. A triangle AMN is inscribed in the triangle OAB, O being the origin, with right angle at N ; M and N lie respectively on OB and AB. If area of Δ AMN is 
of the area of Δ OAB, then 
is equal to-
A
3
B
C
3 or 
D
Text Solution
Verified by ExpertsThe correct answer is:
A
Let 
= λ , Then N ≡ 
Slope of MN is 1, so, equation of MN is
y – 
= x – 
… (i)
Hence, M is 
Area of Δ AMN = 
AN × MN
= 
= 
Area of Δ OAB = 
a 2 . According to given condition
= 
× 
a 2 ⇒ 3x 2 – 10 λ + 3 = 0
⇒ λ = 3, 
.
For λ = 
, M lies outside the segment OB, hence λ = 3.
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