What Is a Semicircle?

What the diameter creates

Semicircles are important in theorem work because an angle inscribed in a semicircle is a right angle. That makes diameter-based diagrams especially valuable in circle geometry.

This page keeps the diameter visible so the semicircle is read from its defining cut, not from a vague half-round picture.

The diameter is the important clue. A curved half-looking piece without a diameter may be a different circle segment, while a diameter guarantees two equal semicircular arcs. The same diameter also creates the right-angle result for an angle whose vertex lies on the semicircle.

The curved boundary of a semicircle has half the circumference of the original circle, while the full region also includes the straight diameter. Be clear whether a question asks for an arc length, a perimeter, or an area, because each includes different pieces.

For a circle of radius 4, the semicircular arc has length 4π, but the perimeter of the half-disk adds the 8-unit diameter. The words arc, perimeter, and area point to different measurements even when they use the same half-circle drawing.

• A semicircle is half of a circle and spans 180 degrees.
• A semicircle is determined by a diameter, not by any random chord.
• The arc of a semicircle measures 180 degrees.
• A point on the semicircle connected to the diameter's endpoints forms a right inscribed angle.

Where semicircles help

• Use semicircles in Thales-type right-angle problems.
• Use them when finding half-circle area, arc length, or perimeter relationships.
• Use them in diagrams where diameter creates two equal circular parts with different theorem consequences.

Semicircle checks to make

• Do not call a region a semicircle unless the dividing line is a diameter.
• Do not confuse a semicircle with a general segment region that only looks cap-shaped.
• Do not ignore whether the problem means the 180-degree arc or the half-disk region.