If `l_(1), l_(2), l_(3)` are respectively the perpendicular from the vertices of a triangle on the opposite side, then show that `l_(1)l_(2) l_(3) =(a^(2)b ^(2) c^(2))/(8R^(3)).`

If l, l_(1), l_(2) and l _(3) be respectively the radii of the in-circle and the three escribed circles of a Delta ABC, then find l_(1)l_(2) l_(3)-l(l_(1)l_(2) +l_(2) l_(3)+l_(1) l_(3)).

Perimeter of equilateral triangle with side 2l is 6l

Let position vectors of point A,B and C of triangle ABC represents be hati+hatj+2hatk, hati+2hatj+hatk and 2hati+hatj+hatk . Let l_(1),l_(2) and l_(3) be the length of perpendicular drawn from the orthocenter 'O' on the sides AB, BC and CA, then (l_(1)+l_(2)+l_(3)) equals

Let L_(1),L_(2),L_(3) be three straight lines a plane and n be the number of circles touching all the lines . Find the value of n.

Evaluate l_(n)= int (dx)/((x^(2)+a^(2))^(n)) .

If r_(1),r_(2) and r_(3) are the position vectors of three collinear points and scalars l and m exists such that r_(3)=lr_(1)+mr_(2) , then show that l+m=1 .

If cosectheta-sintheta=l , and sectheta-costheta=m , show that l^2m^2(l^2+m^2+3)=1 .