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Geometry: Circles


Characteristics of Circles

Tangent Lines and Secant Lines

Problem : What two geometric figures form the boundary of a sector? A circle segment?

A central angle and an arc form the boundary of a sector. A circle segment is bounded by a chord and an arc.

Problem : If a central angle is 45 degrees, what is the measure of the major arc whose endpoints are at the intersection of the central angle and the circle?

315 degrees

Problem : When does a circle segment lie entirely within a sector?

When the arc defined by the central angle of the sector contains the arc defined by the chord that bounds the segment of the circle.

Problem : If two different diameters are drawn into a circle, how many sectors are defined?

Four sectors are defined--the diameters intersection at the center creates four central angles, which define four different sectors.

Problem : If the chord AB is perpendicular to the diameter PQ, and Q lies on the minor arc whose endpoints are A and B, what is the relationship between arc AQ and arc BQ?

They are equal, because the diameter is the perpendicular bisector of the chord AB.