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Chapter 5: Circles and Loci

# The Basics

First, we are going to talk about the circle. A circle is the set of all points in a plane that are a given distance from a fixed point in that plane. The fixed point is the center of the circle. A segment from the center to any point on the circle is a radius. A circle is named by its center. The circle with center point O is called circle O.

When two circles have the same radii, then these two circles are called congruent. Talking about the radius, when set of all points whose distance from center of the circle is less than the radius, it is called the interior of the circle; when set of all points whose distance from the center of the circle is greater than the radius, it is called the exterior of the circle. Two radii form the diameter that is the longest distance in the circle. Diameter is also a kind of chord which is a segment whose endpoints are on the circle. When you extend a chord into both directions, you get a secant. A secant is a line that intersects the circle in two points. A special kind of secant is called tangent that only intersects the circle at one point. The point of intersection is called the point of tangency. Followings are some additional concepts about the chord and tangent:

If a line or segment contains the center of a circle and is perpendicular to a chord, then it bisects the chord.

In the same circle or in congruent circles, congruent chords are equidistant from the centers.

In the same circle or in congruent circles, chords that are equidistant from the centers are congruent.

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