If a triangle has sides $a, b, c$ and $r_1 > r_2 > r_3$ (where $r_1, r_2, r_3$ are the ex-radii),then:

In a $\triangle ABC$,if $r_1 > r_2 > r_3$,then which of the following is true?

In $\triangle ABC$, with usual notations, if $a = 4$, $b = 5$, and $c = 6$, then $\cos A$ and $\cos C$ are calculated using the Law of Cosines. Find the value of $\cos C$ and $\cos A$ to determine the relationship between $\angle C$ and $\angle A$.

If $4$ times the area of a $\triangle ABC$ is $c^2-(a-b)^2$,then $\sin C$ is equal to:

The sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallest one. Then the sides of the triangle are

$\frac{a\cos A + b\cos B + c\cos C}{a + b + c} = $