Every circle hides a triangle. Drag the radius, sweep the angle, and watch a sector split into its triangle and its segment — the same construction that shapes a clock's sweep, an umbrella's ribs, and a grazing horse's reach.
A sector is the slice enclosed by two radii and the arc between them. A segment is the region enclosed by a chord and the arc it cuts off. Every chord and every pair of radii actually creates two such regions — a smaller one (minor) and a larger one (major). Toggle below to see all four.
OAPB (shaded, minor) is bounded by two radii and the near arc. The rest of the disc, OAQB, is the major sector — its angle is 360° − ∠AOB. Unless a question says otherwise, "sector" always means the minor one.
APB (shaded, minor) is bounded by chord AB and the near arc — no radii involved. AQB, on the far side of the same chord, is the major segment. Again, "segment" by itself means the minor one.
A full circle is a sector of 360°. Slice off any angle θ and you get that same fraction of the circle's area and circumference — that's the whole idea behind both formulas.
A segment is a sector with its triangle sliced off: segment = sector − triangle OAB. Toggle the three layers to see exactly what gets subtracted from what.
Three classic NCERT scenes — a sweeping clock hand, a brooch/umbrella cut into equal sectors, and a horse grazing on a rope tied to a fence corner — all reduce to the same sector-area formula.