Chapter 10. A circle is the set of points in a plane that are equal distance, the radius (r), from a...
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Transcript of Chapter 10. A circle is the set of points in a plane that are equal distance, the radius (r), from a...
A circle is the set of points in a plane that are equal distance, the radius (r), from a given point, the center, which is also in the plane.
Twice the radius of a circle is called the diameter of the circle.
r
The center of the circle is point A. A circle is named by its center. This circle is called circle A
Another definition of a radius of a circle is a segment whose endpoints are the center of the circle and a point on the circle. In circle A segment AB is a radius.
AB
Chord of a CircleA chord of a circle is a segment whose endpoints are on the circle.
A
B
CSegment CB is a chord of circle A.
A diameter of a circle is a segment that passes through the center of the circle and whose endpoints are on the circle.Segment DB is a diameter of circle A.
A
B
D
Tangent of a CircleA tangent of a circle is a line that intersects the circle in exactly one point.
A
B
ELine BE is a tangent of circle A.
Point B is the point of tangency.
Secant of a Circle
A secant of a circle is a line, a ray, or a segment that contains a chord of a circle.
A
BC
Line BC is a secant of circle A.
Tell whether the line or segment is best described as a radius, chord, diameter, secant, or tangent of circle C.
Example 1
Coplanar circles that intersect in one point are called tangent circles.
Internally Tangent Circles
Externally Tangent Circles
A line, ray, or segment that is tangent to two coplanar circles is called a common tangent.
Common Tangents
1st Tangent Theorem
A line, a ray, or a segment is tangent to a circle if and only if it is in the same plane as the circle and is perpendicular to a radius of the circle at the point of intersection.
In the diagram, segment AB is a radius of circle A. Is segment BC tangent to circle A? Explain.
Segment BC is tangent to circle A if
segment BC radius AB at pt. B.
Example 4
267 44892 225 60 625 3600 4225
Therefore Δ ABC is not a right Δ and segmentBC is not perpendicular to radius AB.
In the diagram, S is a point of tangency. Find the radius r of circle T.
Example 5
ST SR
22 248 36r r 2 22304 72 1296r r r
1008 72r14 cmr