Question

If the equations of the sides of a triangle are $x+y=0,$ and $\sqrt{3}y+x=0,$ then which of the following is an exterior point of the triangle?

• A. orthocentre
• B. incentre
• C. centrroid
• D. none of these

Answer 1

The correct option is A orthocentre

The lines $y=x$ and $\sqrt{3}y+x=0$ are inclined at ${45}^0$ and ${150}^0,$ respectively, with the positive direction of x-axis.
So, the angle between the two lines is an obtuse angle.
Therefore, orthocentre lies outside the given triangle, whereas incentre and centroid lie within the triangle (In any triangle, the centroid and the incentre lie within the triangle).