# Intersecting Secants Theorem

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?

• The triangle $BOC$ is isosceles and the base angles are 30 degrees. – Catalin Zara May 30 at 17:15
• Another way: for $ABOC$ the sum of angles is $360^\circ$, but $\angle B=\angle C=90^\circ$, so $\angle BOC=180^\circ -\angle CAB=120^\circ$, then apply the cosine rule for $\triangle BOC$ – Alexey Burdin May 30 at 22:28

Join $$O$$ and $$A$$. $$OA$$ bisects $$\angle ABC$$ and so $$\angle OAB=30^\circ$$. What is $$\tan\angle OAB$$?