Using Sine Law, AD and AE can be proved to have equally divided angle BAC into 3 smaller ones, 40 degrees each. However, angles ADE and AED are 70 degrees (exterior angle of triangles), so triangle DAE should be isoscles, not equilateral.
Hello thereddevilsThere's nothing wrong with the question. Just use some simple trigonometry and Pythagoras' Theorem.
Let , and then if is the mid-point of :Also
So using Pythagorasand hence is equilateral.
(by symmetry)
Grandad