Help me find the coordinates of a point $9$ on a circle.

Question

This seems easy. But it isn't. The diameter is given as $16$ and it asks you to find the coordinates of point $9$. It's tempting to say that it is $(4, 4\sqrt{3})$, but that isn't the answer. What the heck am I doing wrong? We can also assume that the area of each segment is equal

Answer 1

$$x=r\cos\theta$$ $$y=r\sin\theta$$

and $$\theta=\frac{\pi}{3}$$

Answer 2

In parametric form, you have $$x=a+r \cos(t) \qquad \text{and} \qquad y=b+r\sin(t)$$ So $$x_9=a+4 \qquad \text{and} \qquad y_9=b+4\sqrt 3$$