The points z₁, z₂, z₃, z₄ in the complex plane are the vertices of a parallelogram taken in order if and only if

The ex-radii $${r_1},{r_2},{r_3}$$ of $$\Delta $$$$ABC$$ are H.P. Show that its sides $$a, b, c$$ are in A.P.

The derivative of an even function is always an odd function.

From the top of a light-house 60 metres high with its base at the sea-level, the angle of depression of a boat is $${15^ \circ }$$. The distance of the boat from the foot of the light house is