In a triangle $ABC$,if $(r_1-r_3)(r_1-r_2)-2r_2r_3=0$,then $a^2-b^2=$

The angles of depression of the top and the foot of a chimney as seen from the top of a second chimney,which is $150 \, m$ high and standing on the same level as the first,are $\theta$ and $\phi$ respectively. If $\tan \theta = \frac{4}{3}$ and $\tan \phi = \frac{5}{2}$,then the distance between their tops is.......$m$.

If $\triangle ABC$ is right-angled at $C$,then the value of $\tan A + \tan B$ is

If in $\Delta ABC$,$2b^2 = a^2 + c^2$,then $\frac{\sin 3B}{\sin B} = $

If the incircle of the $\Delta ABC$ touches its sides at $L, M$ and $N$ respectively,and if $x, y, z$ are the circumradii of the triangles $\Delta MIN, \Delta NIL$ and $\Delta LIM$ respectively,where $I$ is the incentre,then the product $xyz$ is equal to:

In $\triangle ABC$,if $\cos A \cdot \cos B \cdot \cos C = \frac{1}{5}$,then $\tan A \tan B + \tan B \tan C + \tan C \tan A = $