Let the point $A$ lie on the exterior of the circle $k(R).$ From $A$ are drawn the tangents $AB$ and $AC$ to $k.$ The triangle $ABC$ is еquilateral. Find the side of $\triangle ABC$.
Answer: $R\sqrt{3}.$
I am not sure how to approach the problem. We should use the Intersecting Chords Theorem. Can you give me a hint?
Hint:
Join $O$ and $A$. $OA$ bisects $\angle ABC$ and so $\angle OAB=30^\circ$. What is $\tan\angle OAB$?