CHAPTER 10: CIRCLES10.1: Tangents to Circles

LEARNING OUTCOMES I will be able to identify segments and lines

related to circles.

VOCABULARY Circle: A circles is a set of points that are

equidistant from a given point, called the center.

VOCABULARY Radius: This is the distance from the center

of the circle to a point on the circle. Two circles are considered congruent if they

have the same radius.

VOCABULARY Diameter: The diameter is the distance

across the circle through the center. The diameter is twice the radius, or d = 2r.

VOCABULARY Chord: A chord is a segment whose

endpoints are points on a circle. In this example PR and PS are chords.

VOCABULARY Secant: A secant is a line that intersects a

circle in two points.

VOCABULARY Tangent: a tangent line is a line that

intersects a circle at one point. Where the tangent line intersects a circle is called a point of tangency.

COMMON TANGENTS Common tangents are either external or

internal.

Internal External

PRACTICE

ACTIVITY Draw a circle. Draw a line tangent to your circle. Draw the radius to your point of tangency.

Think-Pair-ShareWhat do you notice about the tangent line and the radius?

PROPERTIES OF TANGENT LINES

IS LINE EF TANGENT TO THE CIRCLE?

To determine this we use the Pythagorean Theorem to see if these three lengths form a right triangle.

11 +60² ² = 61² 121 + 3600 3721 = 3721 Since these lengths form a right triangle, EF is tangent to the circle

FIND THE RADIUS OF THE CIRCLE.r + 16 = (r+8) ² ² ²r + 256 = r + 16r + ² ²64-r² -r²256 = 16r + 64192 = 16r12 = r

The radius is 12.

MORE PROPERTIES OF CIRCLES

FIND THE VALUE OF Xx + 2 = 11² - 2 -2x = 9²

x = 3

EXIT TICKET HOMEWORK Tell whether AB is

tangent to the circle. 18-28, 36-41, 46-48

CHAPTER 10.2 Arcs and Chords

LEARNING OUTCOMES I will be able to use arc addition postulate to

find missing arc measurements I will be able to use properties involving

congruent chord/arcs to find missing measurements.

MINOR AND MAJOR ARCS A minor arc is an arc that is less than 180

degrees and is typically expressed with two letters.

A major arc is an arc that is greater than 180 degrees and is typically expressed with three letters.

ARC ADDITION POSTULATE

PRACTICE

THEOREMS

THEOREMS

PRACTICE

22. We can conclude that segment AB and segment CD are equidistant from F.

23. We can conclude that segment AB is congruent to segment CB and that they are equidistant from F.

24. We can conclude that segment AD is congruent to segment BD.

PRACTICE