Question 52
Let $\triangle ABC$ be a triangle. On the sides $BC$, $CA$, $AB$ of the triangle, construct outwardly three squares with centres $O_a$, $O_b$, $O_c$ respectively. Let $\omega$ be the circumcircle of $\triangle O_aO_bO_c$.
Given that $A$ lies on $\omega$, prove that the centre of $\omega$ lies on the perimeter of $\triangle ABC$.
Given that $A$ lies on $\omega$, prove that the centre of $\omega$ lies on the perimeter of $\triangle ABC$.