Question

If in a triangle ABC, the line joining the circumcentre and incentre is parallel to BC, then $\cos A+\cos C$ is equal to

• A. $0$
• B. $1$
• C. $2$
• D. none of these

Answer 1

The correct option is B $1$

$R\cos B=r$

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

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

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

$\cos A+\cos C=1$