There is a circle c, that has a center O, and a circle d that's internally tangent to it. If there are two tangents of d that meet at O, making a $72°$ angle, what's the shortest distance between the d and O?
I used GeoGebra to make this picture, and I can find an approximate answer (it's approximately $0.26$), but some quick tests with bigger numbers revealed more decimals. The orange line segment's length is the shortest distance I want to find.