Let $CX, CY$ be the tangents from vertex $C$ of triangle $ABC$ to the circle passing through the midpoints of its sides. Prove that lines $XY , AB$ and the tangent to the circumcircle of $ABC$ at point $C$ concur.
parmenides51 wrote:
Let $CX, CY$ be the tangents from vertex $C$ of triangle $ABC$ to the circle passing through the midpoints of its sides. Prove that lines $XY , AB$ and the tangent to the circumcircle of $ABC$ at point $C$ concur.
Let $\mathcal{H}$ be the homothety centered at $C$ with power $2$. Denote the new position of an object $P$ with $P’$. Let $\omega$ denote the point circle $C$. Note that the claim follows by applying Radical Axis theorem to $\omega, (X’Y’BA), (ABC)$.