A circle touching all the vertices of a triangle or polygon.
- The three lines through the incircle and the circumcircle of the three triangles meet at a point.
- The circumcircle of a triangle formed by three tangents to a parabola passes through the focus of the parabola.
- Prove that the circumcircles of the triangles BMR and CNR have a common point lying on the side BC.
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