In a right-angled triangle
let
be the altitude drawn to the hypotenuse and let the straight line joining the incentres of the triangles
intersect the sides
at the points
respectively. If
and
dnote the areas of triangles
and
respectively, show that
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In a right-angled triangle $ABC$ let $AD$ be the altitude drawn to the hypotenuse and let the straight line joining the incentres of the triangles $ABD, ACD$ intersect the sides $AB, AC$ at the points $K,L$ respectively. If $E$ and $E_1$ dnote the areas of triangles $ABC$ and $AKL$ respectively, show that
$$\frac {E}{E_1} \geq 2.$$
Školjka