Question 33
Let $\triangle ABC$ be an acute triangle. Let $\omega$ be a circle whose center $L$ lies on the side $BC$. Suppose that $\omega$ is tangent to $AB$ at $B_1$ and to $AC$ at $C_1$. Suppose also that the circumcenter $O$ of the triangle $ABC$ lies on the shorter arc $B_1C_1$ of $\omega$.
Prove that the circumcircle of $ABC$ and $\omega$ meet at two points.
Illustrative configuration only.
Prove that the circumcircle of $ABC$ and $\omega$ meet at two points.
Illustrative configuration only.