When does equality hold?
2. Let the circles 
and 
intersect at two points 
and 
, and let 
be a common tangent of and that touches and at 
and 
respectively. If 
and 
, evaluate the angle 
.
and intersect at two points and , and let be a common tangent of and that touches and at and respectively. If and , evaluate the angle .3. On a board there are 
nails, each two connected by a rope. Each rope is colored in one of given distinct colors. For each three distinct colors, there exist three nails connected with ropes of these three colors.
nails, each two connected by a rope. Each rope is colored in one of given distinct colors. For each three distinct colors, there exist three nails connected with ropes of these three colors.a) Can be 
?
be ?b) Can be 
?
be ? 
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