In the Soddy construction, the triangle vertices form the centers of three mutually tangent circles. There are two circles tangent to those three original circles, the inner and outer Soddy circles, with centers called the Soddy points (not labeled). The two Soddy points define the Soddy line (red), which includes the incenter of .

The Gergonne line and the Soddy line are perpendicular and intersect at the Fletcher point .

Let , and be the circumradius, inradius and semiperimeter of , respectively.

Define (the line is shown in red).

Then .

You can drag the points , and .