Question

In the triangle $ABC$ if the line joining incentre and circumcenter is parallel to $AB$ then the value of $\cos A+\cos B$ is

• A. $0$
• B. $-1$
• C. $1$
• D. $\frac{1-\sqrt{3}}{2}$

Answer 1

The correct option is C $1$

$CO=R\cos C$

$I{O}_1=r$

$R\cos c=r$

$\frac{r}{R}=\cos c$

$r=4R\sin \frac{A}{2}\sin \frac{B}{2}\sin \frac{C}{2}=R\cos c$

$4\sin \frac{A}{2}\sin \frac{B}{2}\sin \frac{C}{2}=\cos c$

$\cos A+\cos B+\cos C-1=\cos C$

$\cos A+\cos B=1$