Circles

A circle is the collection

A circle is the collection of all points in a plane at a fixed distance (radius) from a fixed point (center). Key terms: Center (O), Radius (distance

Theorem 12

Theorem 12.1: Equal chords of a circle subtend equal angles at the center. Proof uses SSS congruence of triangles formed by joining center to endpoint

Theorem 12

Theorem 12.3: The perpendicular from the center of a circle to a chord bisects the chord. Proof method: Join center O to endpoints A, B of chord → Dra

Key principle

Key principle: Through any three non-collinear points, exactly one circle can be drawn. Construction method: Draw perpendicular bisectors of any two s

Theorem 12

Theorem 12.4: The angle subtended by an arc at the center is double the angle subtended by the same arc at any point on the remaining circle. Mathemat