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MathNet 2015-part-02 — 191 problems (EN–VI) Question 166

Math Olympiad Vault · MathNet 2015-part-02 — 191 problems (EN–VI)

Question 166

Through a point $A$ of a circle with centre $O$, a tangent to this circle is drawn, and two points $B$ and $C$ are taken on this tangent, with $C$ between $A$ and $B$. From $B$ and $C$, the tangents $(B D)$ and $(C E)$ to the circle are drawn. Prove that $\widehat{B O C}=\widehat{D A E}$.