Question

Let ABC be a triangle with ∠A = 90◦ and AB = AC. Let D and E be points on the segment
BC such that BD : DE : EC = 1 : 2 : √
3. Prove that ∠DAE = 45◦

Answer 1

Let BD = x , DE = 2x , EC = root 3x => BC = x+ 2x + root 3 x => BC = ( 3+root3) x , now let AB=AC=y By pythagoreous theorem 2y^2 = {(3+root3)x}^2 Now it is easy to prove