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A circle tangent to the circumcircle and two sides

Source: Moldova 2007 IMO-BMO TST IV problem 3

March 25, 2007

geometrycircumcircleincentergeometry proposed

Problem Statement

Let

ABC

be a triangle. A circle is tangent to sides

AB, AC

and to the circumcircle of

ABC

(internally) at points

P, Q, R

respectively. Let

S

be the point where

AR

meets

PQ

. Show that

\angle{SBA}\equiv \angle{SCA}