The fifth proof even captures both isosceles and non-isosceles triangles in one go. As if that was not enough, the pair also ...

Angle OGH (\(y\)) = angle OHG because triangle GOH is also isosceles. Lengths OH and OG are also both radii. Angle GOH = \(180^\circ - 2y\) (because angles in a triangle add up to 180°).