The vertices of an equilateral triangle are labelled \(X\), \(Y\) and \(Z\). The points \(X\), \(Y\) and \(Z\) lie on a circle of circumference \(10\) units. Let \(P\) and \(A\) be the numerical values of the triangle’s perimeter and area, respectively. Which of the following is true?

\(\dfrac{A}{P}=\dfrac{5}{4\pi}\);

\(P<A\);

\(\dfrac{P}{A}=\dfrac{10}{3\pi}\);

\(P^2\) is rational.

Can we draw a diagram? What is the radius of the circle?