Let ABC be a triangle such that cos A=`2/3` and cosB=`3/4`,then
| A. |
ABC is an acute-angled triangle |
| B. |
tan A + tan B + tan C `>=3sqrt3` |
| C. |
Orthocentre of the triangle lies outside its circumcirles |
 |
| D. |
`cos^2A +cos^2B +cos^2C<=1` |
cos C = – cos (A + B)
= sin a sin B – cos A cos B
`=sqrt5/3xxsqrt7/4-2/3xx3/4`
=`(sqrt5-6)/12<0`
Thus, `/_C` is an obtuse angle. Now, in any obtuse-angled triangle, the orthocentre lies outside the circumcircle of the triangle.