1. Given a digits {
} . Find the number of numbers of 6 digits which cantain 
or 's digit and they is permulated (For example 137456 and 314756 is one numbers).
} . Find the number of numbers of 6 digits which cantain or 's digit and they is permulated (For example 137456 and 314756 is one numbers). 
3. Given 
is not isosceles triangle. 
and 
its incenter and circumcenter. The incircle tangents to 
at a point 
. The circumcircle of 
intersects 
at 
. Prove that 
, where 
is radius of incircle of .
is not isosceles triangle. and its incenter and circumcenter. The incircle tangents to at a point . The circumcircle of intersects at . Prove that , where is radius of incircle of . 
5. Given points 
and lie a circle. 
. 
and 
incenters of 
. 
midpoints of arcs 
. Then prove that 
are concurrent.
Πηγή: artofproblemsolving
and lie a circle. . and incenters of . midpoints of arcs . Then prove that are concurrent.Πηγή: artofproblemsolving
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