geometry: chapter 10 10.1: tangents to circles. a circle is the set of all points in a plane that...
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GEOMETRY: Chapter 1010.1: 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. 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 from:http://www.pecoglassbending.com/images/Circle%20terms.jpg
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.edu/STUDENT/bakerl3/secant_tangent.gif
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.
. b.
. d.
a DC BD
c DE AE�������������� �
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.
. b.
. d.
a DC BD
c DE AE�������������� �
Ex.2: Use the diagram to find the given lengths.
a. Radius of circle B
b. Diameter of circle A
c. Radius of circle A
d. Diameter of circle B
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 653.
Ex.2: Use the diagram to find the given lengths.
a. Radius of circle B
b. Diameter of circle A
c. Radius of circle A
d. Diameter of circle BAnswer: a) 3 units; b) 4 units; c) 2 units; d) 6 units
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 653.
COPLANAR CIRCLES—Two 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.
Common Tangents—A 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
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.
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.
Theorem 10.1and 10.2:
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 653.
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.
Ex.4:
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 653.
In the diagram, is a radius of circle A.
Is tangent to circle A? Explain.
AB
BC
Ex.4:
Answer:No. 252+ 602=4225, but 672=4489
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 653.
In the diagram, is a radius of circle A.
Is tangent to circle A? Explain.
AB
BC
Ex.5:
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 654.
In the diagram, S is a point of tangency.
Find the radius r of circle T.
Ex.5:
Answer: 14 cm
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 654.
In the diagram, S is a point of tangency.
Find the radius r of circle T.
Theorem 10.3:
Image taken from:http://www.partnership.mmu.ac.uk/cme/Geometry/CircleGeom/Images/Tangent.jpg
Tangent Segments from a common external point are congruent.
Ex.6:
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 654.
In circle C, is tangent at A and
is tangent at B. Find x.
DA
DB
Ex.6:
Answer: 5.5
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 654.
In circle C, is tangent at A and
is tangent at B. Find x.
DA
DB
10.1, p. 599, #6-29 all