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GEOMETRY: Chapter 10

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GEOMETRY: Chapter 10 10.1: Tangents to Circles A circle is the set of all points in a plane that are equidistant from a given point called the center of the circle. – PowerPoint PPT presentation

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Title: GEOMETRY: Chapter 10


1
GEOMETRY Chapter 10
  • 10.1 Tangents to Circles

2
  • A circle is the set of all points in a plane that
    are equidistant from a given point called the
    center of the circle. A circle with center P
    can be written P. A segment whose endpoints are
    the center of any point on the circle is a
    radius.
  • A chord is a segment whose
  • endpoints are on a circle.
  • A diameter is a chord that
  • contains the center of a circle.


Image taken fromhttp//www.pecoglassbending.com/i
mages/Circle20terms.jpg
3
  • A secant is a line that intersects a circle in
    two points. A tangent is a line in the plane of a
    circle that intersects the circle in exactly one
    point, the point of tangency. The tangent ray and
    the tangent segment are also called tangents.


Image taken from http//literacy.calumet.purdue.e
du/STUDENT/bakerl3/secant_tangent.gif
4
  • Ex.1
  • Tell whether the line or segment is best
    described as a radius, chord, diameter, secant,
    or tangent of circle C.

Image taken from Geometry. McDougal Littell
Boston, 2007. P. 652.
5
  • Ex.1
  • Tell whether the line or segment is best
    described as a radius, chord, diameter, secant,
    or tangent of circle C.
  • Answer a) radius b) secant c) diameter d)
    tangent

Image taken from Geometry. McDougal Littell
Boston, 2007. P. 652.
6
  • Ex.2 Use the diagram to find the given lengths.
  • Radius of circle B
  • Diameter of circle A
  • Radius of circle A
  • Diameter of circle B

Image taken from Geometry. McDougal Littell
Boston, 2007. P. 653.
7
  • Ex.2 Use the diagram to find the given lengths.
  • Radius of circle B
  • Diameter of circle A
  • Radius of circle A
  • Diameter of circle B
  • Answer a) 3 units b) 4 units c) 2 units d) 6
    units

Image taken from Geometry. McDougal Littell
Boston, 2007. P. 653.
8
  • COPLANAR CIRCLESTwo circles can intersect in two
    points, one point, or two points. Coplanar
    circles that intersect in one point are called
    tangent circles. Coplanar circles that have a
    common center are called concentric.


Image taken from Geometry. McDougal Littell
Boston, 2007. P. 652.
9
  • Common TangentsA line, ray, or segment that is
    tangent to two coplanar circles is called a
    common tangent.


Image taken from http//mtl.math.uiuc.edu/modules
/dynamic/lessons/les4_7.gif
10
  • Ex.3 Tell how many common tangents the circles
    have and draw them.
  • Answer a. 2 common tangents b. 4 common c. 3
    common tangents

Image taken from Geometry. McDougal Littell
Boston, 2007. P. 653.
11
  • Ex.3 Tell how many common tangents the circles
    have and draw them.
  • Answer a. 2 common tangents b. 4 common c. 3
    common tangents

Image taken from Geometry. McDougal Littell
Boston, 2007. P. 653.
12
  • Theorem 10.1and 10.2

In a plane, a line is tangent to a circle if and
only if the line is perpendicular to a radius of
the circle at its endpoint on the circle.
Image taken from Geometry. McDougal Littell
Boston, 2007. P. 653.
13
  • Ex.4

Image taken from Geometry. McDougal Littell
Boston, 2007. P. 653.
14
  • Ex.4
  • AnswerNo. 252 6024225, but 6724489

Image taken from Geometry. McDougal Littell
Boston, 2007. P. 653.
15
  • Ex.5

Image taken from Geometry. McDougal Littell
Boston, 2007. P. 654.
16
  • Ex.5
  • Answer 14 cm

Image taken from Geometry. McDougal Littell
Boston, 2007. P. 654.
17
  • Theorem 10.3

Tangent Segments from a common external point are
congruent.
Image taken fromhttp//www.partnership.mmu.ac.uk/
cme/Geometry/CircleGeom/Images/Tangent.jpg
18
  • Ex.6

Image taken from Geometry. McDougal Littell
Boston, 2007. P. 654.
19
  • Ex.6
  • Answer 5.5

Image taken from Geometry. McDougal Littell
Boston, 2007. P. 654.
20
  • 10.1, p. 599, 6-29 all
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