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MathNet 2008-part-05 — 164 problems (EN–VI) Question 57

Math Olympiad Vault · MathNet 2008-part-05 — 164 problems (EN–VI)

Question 57

On the circumcircle of $A B C$, let $A'$ be the midpoint of arc $B C$ (not containing $A$).

a. Show that $A, I, A'$ are collinear.

b. Show that $A'$ is the circumcenter of $BIC$.