Just a theorem

Geometry Level 4

Let $\triangle ABC$ be an equilateral triangle inscribed in a circle and $P$ a point on the minor arc $BC$ . Let $PB=a$ and $PC=b$ . Find the side length of the triangle $\triangle ABC$ .

Inspiration.

\sqrt{ab}

\sqrt{a^2-ab+b^2}

\sqrt{a^2+ab+b^2}

\dfrac{a+b}{2}

\dfrac{ab}{a+b}