In the figure below, what value on X provides the maximum angle α?
2026-03-25 04:36:35.1774413395
For what value on X provides the maximum angle α
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The vertex of angle $\alpha$ (point $G$ in diagram below) is constrained on a line parallel to $BF$ and vertically shifted by $1$. If $r$ is the radius of circle $GCD$, then $\sin\alpha=8/r$ and $\alpha$ gets then its maximum when the radius of the circle is minimum, that is when circle $GCD$ is tangent to the line of $G$.
From this geometric condition it is not difficult to find $r$ and then $\alpha$.