When a triangle is formed inside a semicircle, two lines from either side of the diameter meet at a point on the circumference at a right angle. The angle in a semicircle is a right angle of \(90 ...

More simply, the angle at the centre is double the angle at the circumference. Angle OGK (\(x\)) = angle OKG because triangle GOK is also isosceles. Lengths OK and OG are also both radii.