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MathNet 2008-part-02 — 165 problems (EN–VI) Question 108

Math Olympiad Vault · MathNet 2008-part-02 — 165 problems (EN–VI)

Question 108

Put 6 points $A$, $B$, $C$, $D$, $E$, $F$ on the circumference of a circle in this order in such a way that the following conditions are satisfied: arc $AB$ and arc $BC$, arc $CD$ and arc $DE$, and arc $EF$ and arc $FA$ have same lengths, respectively. Determine the value of the angle $\angle BFD$ if $\angle ACE = 68^\circ$. (Caution: the following diagram may not be accurate.)

Question illustration