olympiad level probo...

In an isocelous right-angled triangle ABC, right angled at A, M and N are two points on BC such that

BM² + CN² = MN² then prove that, LMAN = 45Â°

3 Answers

This isn't much difficult if use identities like tan(a-b) shamelessly ..:P

@ Rahul: Once upon a time in TIIT , u had given this to me ,remember ?:D

u know yesterday... i just got muddled in this probo... i just cracked much of it... but failed at last...

so finally i saw its solution.... Its an RMO probo...

Tommoow m having my board exam of science....

and so not concentrating much on this...

well these problems are nothing but just a game of construction...!!

Its an RMO 2003 problem..!!

The construction goes this way... Owww my God...!!

√ √ || {} [] () → ~ ^ x x x → → ln log lg lim lim cos sin tan cot arcsin arccos arctan

∫ ∫ ∫ ∫ ∫ ∬ ∬ ∬ ∬ ∬ ∭ ∭ ∭ ∭ ∭ ⨌ ⨌ ⨌ ⨌ ⨌

∑ ∑ ∑ ∑ ∑ ∮ ∮ ∮ ∮ ∮ ∏ ∏ ∏ ∏ ∏ ∐ ∐ ∐ ∐ ∐

+ - × ÷ ± ∓ = ∪ ∩ ≠ ∼ ≈ ∅ ∀ ∃ ∈ ∋ ∝ ≤ ≥ ≃ ≅ ≡ < > ≪ ≫ ⊂ ∉ ⊃ ⊆ ⊇ ⇒ ⇐ ⇔ ⇒ ⇐ ⇔ ⇑ ⇓ ⇕ → ← ↔ → ← ↔ ↑ ↓ ↕ ↖ ↗ ↘ ↙ ↪ ↩ ⇀ ↼ ⇁ ↽

° ∂ ∞ α β γ δ θ λ μ ν ξ π ρ σ φ ω ε ƒ κ τ υ Γ Δ Λ Σ Π Ω