# Finding the change of the area of the triangle from moving a point

Point C moves along the top arc of a circle of radius 1 centered at the origin O(0, 0) from point A(-1, 0) to point B(1, 0) such that the angle BOC decreases at a constant rate 1 radian per minute. How does the area of the triangle ABC change at the moment when |AC|=1? Answer: it increases at 1/2 square units per minute. Could you give me a hint how to solve this task? I don't even know what to begin with.

Say angle $BOC$ is $\theta$. Express the area of triangle $ABC$ in terms of $\theta$ (use $\sin$). This is an area $A$ in terms of $\theta$. Find $\frac{dA}{d\theta}$.Then find the point where $CA = 1$ and determine $\theta$ at that point. Evaluate $\frac{dA}{d\theta}$ for that value of $\theta$.
• and then use the chain rule to obtain $\frac{dA}{dt} = \frac{dA}{d\theta}*\frac{d\theta}{dt}$ – Quark Oct 16 '16 at 18:13