In the triangle-bisection illusion, a dot is inscribed exactly halfway up the height of an equilateral triangle, but it looks apparently far more than halfway up. The illusion is found for second-order triangles defined by stereo depth and by equiluminous texture. It is strongest for equilateral triangles, and even stronger for concave triangles with curved sides. We propose that the observers are probably responding to the centre of area or centre of gravity of the triangle rather than to its half-height.