# From Perpendicular Center Lines to Concyclic Points

### Solution

The problem is easily solved by angle chasing. Observe the presence of several cyclic quadrilaterals, e.g.,

This explains an interesting distribution of equal angles:

Recombining suitable angles we see that the opposite angles at the four points of tangent intersections do indeed add up to $180^{\circ},\,$ making the points concyclic.

### Acknowledgment

The problem has been kindly posted by Dao Thanh Oai at the CutTheKnotMath facebook page.