I need help on this second part to this question...

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Q: Sketch the curve with the equation $\displaystyle r=a(1+ \cos\theta)$ for $\displaystyle 0 \le \theta \le \pi $ where $\displaystyle a>0$. Sketch also the line with the equation $\displaystyle r=2a \sec \theta$ for $\displaystyle - \frac{\pi}{2} < \theta < \frac{\pi}{2} $ on the same diagram.

The half-line with the equation $\displaystyle \theta = \alpha$, $\displaystyle 0<\alpha<\frac{\pi}{2}$, meets the curve at $\displaystyle A$ and the line with equation $\displaystyle r=2a \sec \theta$ at $\displaystyle B$. If $\displaystyle O$ is the pole, find the value of $\displaystyle \cos \alpha$ for which $\displaystyle OB=2OA$.

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I've drawn the graph but can't do the second part to the question. Can someone help please? Thank you in advance.