I have two concentric circles, one smaller and one larger. I need to geometrically construct a circular sector that will touch the outer and inner circles at its ends. The conditions are as follows:
- At the outer end, the angle between the sector and the tangent to the circle should be 30 degrees.
- At the inner circle, the sector should be perpendicular (i.e., it should point towards the center of both circles).
In terms of construction, this involves constructing a circle X that is tangential (touches line L at point P) and is also perpendicular to circle C (touches an imaginary line M that passes through the center of circle C, but we don't know this line; the imaginary line M is not parallel to line L).
I'm struggling with how to approach this problem. Any guidance or suggestions would be greatly appreciated.