In $\triangle A B C$, if $A B: B C: C A=6: 4: 5$, then $R: r$ is equal to

If $(\alpha, \beta)$ is the orthocentre of the triangle with the vertices $(2,2),(5,1),(4,4)$, then $\alpha+\beta=$

In $\triangle A B C$, if $4 r_1=5 r_2=6 r_3$, then $\sin ^2 \frac{A}{2}+\sin ^2 \frac{B}{2}+\sin ^2 \frac{C}{2}=$

In $\triangle A B C, r_1 \cot \frac{A}{2}+r_2 \cot \frac{B}{2}+m_3 \cot \frac{C}{2}=$