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Chapter 5: Circles and Loci

In the same circle or congruent circles, if two chords are unequally distant from the centers, then the chord nearer its corresponding center is the longer chord.

In the same circle or congruent circles, if two chords are unequal in length, then the longer chord is nearer the center of its circle.

A polygon whose sides are chords of a circle is an inscribed polygon. The polygon is inscribed in the circle; the circle is circumscribed about the polygon.

If a line is perpendicular to a radius at its endpoint on the circle, then the line is tangent to the circle.

A tangent segment is a segment that contains a point of tangency and another point of tangent line to a circle.

If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency.

Two segments drawn tangent to a circle from an exterior points are congruent.

The angle between two tangents to a circle from an exterior point is bisected by the segment joining its vertex to the center of the circle.

A polygon whose sides are tangent to a circle is a circumscribed polygon. The polygon is circumscribed about the circle, and the circle is inscribed in the polygon.

A line tangent to each of two coplanar circles is a common tangent.

Two coplanar circles are tangent to each other if they are tangent to the same line at the same point.

# Sphere

When you put a circle into space and turn it 360 degree, you get a sphere. A sphere is the set of all points in space that are given distance from a fixed point. The fixed point is the center of the sphere. A segment from the center of the sphere to any point on the sphere is a radius of the sphere. A chord of a sphere has endpoints on the sphere. A secant of a sphere is a line that intersects the sphere in two points. A line or plane that intersects a sphere in exactly one point is tangent to that sphere

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