Hubert Shutrick

To construct a circle tangent to two given lines a given circle.

The diagram shows a construction for a circle that is tangent to a given circle c(BLDK) and given lines BD and LK. Since it is known that this circle exists, we can consider the homothety taking it to the circle c projecting from their common point S. It takes BD to a parallel tangent to c that is well determined although we do not know the common point S. There is another well-determined tangent that is the image of LK. These two tangents meet at the image R of the intersection J of BD and LK so S is where RJ meets c.