Question

In triangle $ABC$, line joining the circumcentre and orthocentre is parallel to side $AC$,then $\cos A+\cos C$ is equal to

• A. -1
• B. 1
• C. -2
• D. 2

Answer 1

The correct option is B 1

Given , line joining orthocentre and circumcentre to side AC

We know $R\cos B=r,\frac{r}{R}=\cos B$

$\frac{r}{R}=4\sin \frac{A}{2}\sin \frac{B}{2}\sin \frac{C}{2}=\cos B\cos A+\cos B+\cos C-1=\cos B\cos A+\cos C=1$