Question 79
Let $ABC$ be a triangle with median $AK$. Let $O$ be the circumcenter of the triangle $ABK$.
a) Prove that if $O$ lies on a midline of the triangle $ABC$, but does not coincide with its endpoints, then $ABC$ is a right triangle.
b) Is the statement still true if $O$ can coincide with an endpoint of the midsegment?
a) Prove that if $O$ lies on a midline of the triangle $ABC$, but does not coincide with its endpoints, then $ABC$ is a right triangle.
b) Is the statement still true if $O$ can coincide with an endpoint of the midsegment?