Triangle Squared

Geometry Level 5

Let \(ABC\) be a triangle, and construct squares \(ABXY\) and \(ACWZ\) on the exterior of triangle \(ABC\). Also, let \(AD\) be the altitude, and \(T\) the intersection of line segments \(AD\) and \(YZ.\)

If \(BC = 4,\) then find the length of \(AT.\)