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I have a problem that involves construction with the ruler and compass. I want to prove more constructions of the regular pentagon. I finished demonstrating some more constructions, but I couldn’t do one of them. Here is the problem: considering the following points in plan $O(0,0)$, $A(-\frac{1}{2},0)$ and $B(0,1)$. The bisector of the angle $OAB$ intersects the axis $Oy$ in the point $D$. Then, we intersect the horizontal line, which intersects the point $D$ with the trigonometric circle. What I want to prove is that this construction gives us the side of the regular pentagon. I will be grateful if you could help me with some suggestions.

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This image from Wikipedia confirms that it does:

Richmond's construction of pentagon side

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