Inscribed angle theorem

The inscribed angle theorem states that an angle formed by two chords meeting on a circle measures half the central angle subtending the same arc.

Central angle: An angle whose vertex is the center of a circle and whose sides are radii. Its measure is twice that of an inscribed angle subtending the same arc.
Thales' theorem: A theorem stating that an angle subtended by a diameter at the circumference is a right angle. It is the inscribed angle theorem applied to a 180-degree central angle.
Chord (geometry): A line segment whose endpoints lie on a circle. The theorem’s inscribed angle is formed by two chords.
Exterior angle of a circle: An angle formed by two secants, a secant and a tangent, or two tangents meeting outside a circle. Its measure depends on the difference between intercepted arcs, not half one arc.
Inscribed angle: An angle whose vertex lies on a circle and whose sides are chords. It is the angle whose measure the theorem relates to a central angle.
Inscribed circle problem: A geometry problem involving angles or lengths defined by points on a circle. The theorem converts a known arc or central angle into an inscribed angle.
Radius: A line segment from a circle’s center to a point on its circumference. Equal radii create the isosceles triangles used in a standard proof.
Intersecting chords theorem: A theorem stating that products of the segments of intersecting chords are equal. It concerns chord lengths where chords meet inside a circle rather than angles on its circumference.
Isosceles triangle: A triangle with at least two sides of equal length. Radii form isosceles triangles that explain the angle relationship.
Circle geometry: The branch of geometry concerned with circles, their chords, arcs, tangents, and angles. The theorem is a basic tool for solving problems about angles on circles.

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