Let-ABC-be-an-acute-triangle-The-interior-bisectors-of-the-angles-B-and-C-meet-the-opposite-sides-at-the-points-L-and-M-respectively-Prove-that-there-exists-a-point-K-in-the-interior-of-the-side-

Question Number 16874 by Tinkutara last updated on 27/Jun/17

Let A B C be an acute triangle . The

interior bisectors of the angles ∠ B and

∠ C meet the opposite sides at the

points L and M, respectively . Prove

that there exists a point K in the

interior of the side B C such that

Δ K L M is equilateral if and only if

∠ A = 60 ° .