Review question

# If these centres lie on a line, why is the triangle isosceles? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R8917

## Interactive diagram

In a triangle $ABC$, $I$ is the incentre, $H$ the orthocentre, and $O$ the circumcentre. Prove that $AI$ bisects $\angle OAH$. Hence, or otherwise, prove that if $O$, $H$ and $I$ are collinear the triangle must be isosceles.