Question 5
In a right-angled triangle $ABC$, let $AD$ be the altitude drawn to the hypotenuse and let the straight line joining the incenters of the triangles $ABD$, $ACD$ intersect the sides $AB$, $AC$ at the points $K$, $L$ respectively. If $E$ and $E_1$ denote the areas of the triangles $ABC$ and $AKL$ respectively, show that $\frac{E}{E_1}\ge2$.