# Point C moves along the top arc of a circle of radius 1 centered at the origin O(0, 0) from point A(

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.
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stigliy0
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 $\theta$.
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polivijuye
and then use the chain rule to obtain $\frac{dA}{dt}=\frac{dA}{d\theta }\ast \frac{d\theta }{dt}$