Circles — All Properties

GRE Quantitative · Axiom Academy

LESSON Circles — All Properties Circumference, arcs, sectors, and angles — every circle fact on the GRE traces back to one shape, unrolled and sliced. 1. Circumference Is Just the Rim, Unrolled The radius (r) is the distance from center to rim; the diameter (d) is twice that, straight across through the center. The circumference — the distance all the way around — sounds like it should need a new idea, but watch what happens when the rim peels open and stretches flat: it becomes a straight segment of length exactly . Circumference — in terms of radius or diameter Area — in terms of radius squared 2. Arcs and Sectors — Slices of the Whole An arc is a piece of the circumference; a sector is the matching pie-slice of area, bounded by two radii and that arc. Both are simply the FRACTION of the full circle that the central angle represents, out of the full 360°. Circle of radius 6, arc measure 60°: fraction of the circle is . Arc length = = . Sector area = = . Thin sliver — both arc length and sector area near 0. Full circle — arc length = full circumference, sector area = full area. 3. The Inscribed Angle Is Always Half the Central Angle

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