Circles have a rich set of relationships between central angles, inscribed angles, chords, tangents, and arcs.
A circle is all points equidistant from the center. Radius (r), diameter (d=2r), chord (segment with both endpoints on circle), arc (part of the circle), tangent (line touching at one point).
Circumference C = 2πr = πd. Area A = πr². Arc length = (θ/360°) × 2πr. Sector area = (θ/360°) × πr².
A central angle = its intercepted arc. An inscribed angle = ½ its intercepted arc. Inscribed angles intercepting the same arc are equal. An inscribed angle in a semicircle = 90°.
Two chords intersecting inside a circle: products of segments equal. A tangent from an external point: both tangent segments equal. A tangent is perpendicular to the radius at the point of tangency.
Q1: A central angle of 90° intercepts an arc of:
Q2: An inscribed angle intercepts an arc of 100°. The angle measures:
Q3: A circle has radius 7. Its area is: