If `p_(1),p_(2),p_(3)` are the perpendiculars from the vertices of a triangle to the opposite sides, then prove that
`p_(1)p_(2)p_(3)=(a^(2)b^(2)c^(2))/(8R^(3))`

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 p_(1), p _(2), p_(3) are respectively the perpendicular from the vertices of a triangle to the opposite sides, then find the value of p_(1) p_(2)p _(3).

If p_(1), p_(2),p_(3) are respectively the perpendiculars from the vertices of a triangle to the opposite sides , then (cosA)/(p_(1))+(cosB)/(p_(2))+(cosC)/(p_(3)) is equal to

If the lengths of the perpendiculars from the vertices of a triangle ABC on the opposite sides are p_(1), p_(2), p_(3) then prove that (1)/(p_(1)) + (1)/(p_(2)) + (1)/(p_(3)) = (1)/(r) = (1)/(r_(1)) + (1)/(r_(2)) + (1)/(r_(3)) .

If p_(1),p_(2),p_(3) are the altitues of a triangle from the vertieces A,B,C and Delta is the area of the triangle then prove that (1)/(p_(1))+(1)/(p_(2))-(1)/(p_(3))=(2ab)/((a+b+c)Delta)"cos"^(2)(C)/(2)

If p_(1),p_(2),p_(3) are altitudes of a triangle ABC from the vertices A,B,C and triangle the area of the triangle, then p_(1)^(-2)+p_(2)^(-2)+p_(3)^(-2) is equal to

If p_(1),p_(2),p_(3) are altitudes of a triangle ABC from the vertices A,B,C and ! the area of the triangle, then p_(1).p_(2),p_(3) is equal to

If p_(1), p_(2) and p_(3) are the altitudes of a triangle from the vertices of a Delta ABC and Delta is the area of triangle, prove that : (1)/(p_(1)) + (1)/(p_(2)) - (1)/(p_(3)) = (2ab)/((a+b+c)Delta) cos^(2).(C )/(2)

P_(1) and P_(2) are the lengths of the perpendicular from the foci on the tangent of the ellipse and P_(3) and P_(4) are perpendiculars from extermities of major axis and P from the centre of the ellipse on the same tangent, then (P_(1)P_(2)-P^(2))/(P_(3)P_(4)-P^(2)) equals (where e is the eccentricity of the ellipse)

If p_1,p_2,p_3 re the altitudes of the triangle ABC from the vertices A, B and C respectivel. Prove that (cosA)/p_1+(cosB)/p^2+(cosC)/p_3 =1/R