hemisphere
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An equator is a circle that divides the surface of an object into two equal halves. The term is usually used to explain the circle that divides a plane,t like the Earth, in to two hemispheres.
diameter
Only the diameter can divide the circle in to two equal parts.
A line segment that divides a circle in two is a chord.If the two parts of the circle are equal, the line segment is a diameter.See 'The Parts of the Circle' in Sources and related links, below.
Bisector.