Question

In an isosceles triangle the circumcentre, the orthocentre, the incentre and the centroid are:

• A. Collinear
• B. Coincide
• C. Do not coincide
• D. None of above

Answer 1

The correct option is A Collinear

In $△ABC$, we have

$AB=AC$

Now, we take $AD\perp BC$.

Clearly, $BD=DC$ and $\angle BAD=\angle DAC$

So, clearly, the circumcentre, orthocentre, incenter and centroid lie on the same line $AD$.

Hence, it is said that in an isosceles triangle circumcentre, orthocentre, incenter and centroid are collinear.