Circles Summary

Geometry · Axiom Academy

SUMMARY Unit 5 Summary: Circles Everything about the circle — its parts, its angles, and the formulas that measure it — pulled together in one place. Every circle is built from a handful of parts: the radius , diameter ( d = 2r ), chord , arc , sector , tangent , and secant . An inscribed angle is always half the central angle that cuts off the same arc — and an angle inscribed in a semicircle is always (Thales' theorem). A tangent is perpendicular to the radius at the point of contact, and two tangents drawn from one external point are equal in length. Arc length and sector area are both just a fraction of the whole circle's circumference and area. The standard circle equation (x-h)^2 + (y-k)^2 = r^2 encodes center (h,k) and radius r directly — circles meet coordinate geometry here. One diagram, every part — the vocabulary the whole unit is built on. Core Concept Parts of a Circle A chord joins two points on the circle; the longest chord is the diameter , which passes through the center. An arc is a piece of the circle itself, a sector is the "pie slice" between two radii, and tangent / secant lines touch the circle once or cut it twice. Remember: a radius goes center→edge; a diameter goes edge→edge through the center. Watch out for: an arc is curved length; a chord is the straight segment beneath it. Core Concept Central vs. Inscribed Angles

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