Given a Circle, What is the probability to draw a chord larger than the length of an equilateral triangle inscribed in the circle.

All chords with midpoint in the smaller circle meet the requirement.[br]Would that mean the answer is [math]\frac{1}{4}[/math]?[br][br]So which is it - [math]\frac{1}{2}[/math], [math]\frac{1}{3}[/math] or [math]\frac{1}{4}[/math]? [br](for the previous two methods, see [url=https://beta.geogebra.org/m/W3av3g5n#material/zGNYbyYW]here [/url]and [url=https://beta.geogebra.org/m/W3av3g5n#material/JrtK9W3q]here[/url])