E-AP04 · The boundary after a cut
A wedge of angle \(\theta\), with \(0<\theta<2\pi\), is removed from a disk of radius \(7\) cm. Both straight cut edges are exposed.
Express the perimeter \(L\) of the remaining region in terms of \(\theta\).
The new perimeter is \(6\) cm greater than the original circumference. Find \(\theta\) and the remaining area.
Find all \(\theta\) for which removing the wedge increases the perimeter.
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