If the angles $A, B, C$ of a triangle are in $A.P.$ and the sides $a, b, c$ opposite to these angles are in $G.P.$,then $a^2, b^2, c^2$ are in

In $\triangle ABC$, right-angled at $A$, the circumradius, inradius, and radius of the excircle opposite to $A$ are respectively in the ratio $2:5:\lambda$. Then the roots of the equation $x^2-(\lambda-5)x+(\lambda-6)=0$ are:

In a triangle $ABC$,with usual notations,the sides $a, b, c$ are the roots of the equation $x^3-11x^2+38x-40=0$. Then,find the value of $\frac{\cos A}{a}+\frac{\cos B}{b}+\frac{\cos C}{c}$.

In a triangle $ABC$,if $A, B$ and $C$ are in arithmetic progression,$rr_3 = r_1 r_2$ and $c = 10$,then $a^2 + b^2 + c^2 =$

If $\alpha$ and $\beta$ are different values of $x$ satisfying $a \cos x + b \sin x = c,$ then $\tan \left( \frac{\alpha + \beta}{2} \right) = $

The circumradius $R$ of an isosceles triangle $ABC$ is four times its inradius $r$. If $A = B$,then which of the following is true?