If the lengths of the sides of a triangle are $3, 5, 7,$ then the largest angle of the triangle is

In $\Delta ABC,$ if $8{R^2} = {a^2} + {b^2} + {c^2},$ then the triangle is

In a triangle $ABC$,with usual notations,if $a=4, b=8, \angle C=60^{\circ}$,then the value of $\angle B$ and the ratio $\cos A : \cos C$ respectively are,

In any $\triangle ABC$, the expression $\frac{(a+b+c)(b+c-a)(c+a-b)(a+b-c)}{4b^2c^2}$ is equal to:

If ${p_1}, {p_2}, {p_3}$ are altitudes of a triangle $ABC$ from the vertices $A, B, C$ respectively and $\Delta$ is the area of the triangle,then ${p_1}^{-2} + {p_2}^{-2} + {p_3}^{-2}$ is equal to

In a $\triangle ABC$,if $r_1 = 2r_2 = 3r_3$,then the ratio $a : b$ is: