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

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 • Can you explain to me how you got that? That is also not an option for an answer. – brandon Apr 25 at 22:29
• Welcome to Math.SE. Where is the origin of the coordinates? – Ertxiem Apr 25 at 23:01
• The question doesn't give you the origin of the coordinates, which is why it becomes all the more difficult – brandon Apr 25 at 23:18
• Can you please write down all text of the question? From what you've shown, I would say that your answer is correct. – Ertxiem Apr 25 at 23:29

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