Three semi-circles have a common diameter, each touches the other
two and two lie inside the biggest one. What is the radius of the
circle that touches all three semi-circles?
The square ABCD is split into three triangles by the lines BP and
CP. Find the radii of the three inscribed circles to these
triangles as P moves on AD.
For any right-angled triangle find the radii of the three escribed
circles touching the sides of the triangle externally.
What about an inradius of 4 or 5 or ...?