Geometric constraint solving has applications in a wide variety of fields

such as mechanical engineering

chemical molecular conformation

geometric theorem proving

and surveying. There are mainly three approaches to geometric constraint solving: numerical approach

symbolic approach and constructive approach. Since the constructive approach are simple and practicable

most parametric design take the constructive approach as the basic approach. In the light of the shortage of using only line and circle (rule and compass) as basic drawing tools in constructive approach

in this paper

we introduce a class of new drawing tools: conics. We prove that the class of diagrams within the drawing scope of this new tool is larger than that can be drawn with line and circle. Actually

we prove that a diagram can be drawn with conics if and only if this diagram can be described with a sequence of triangulated equations of degree less than or equal to four. This allows us to maintain the elegance of geometric constraint solving with ruler and compass

because the solutions of cubic and quartic equations can be written explicitly with radicals.