Download presentation
Presentation is loading. Please wait.
1
Lesson 9-2 Tangents (page 333)
Essential Question How can relationships in a circle allow you to solve problems involving segments, angles, and arcs?
2
Tangents
3
Theorem 9-1 If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency. O m T
4
This theorem is proven with an indirect proof
This theorem is proven with an indirect proof. Also, this is why the tangent term is used in trigonometry. If O is a unit circle, the radius = 1, then … O 1 m T Z
5
Tangents to a circle from a point are congruent .
Corollary Tangents to a circle from a point are congruent . A P O B
6
The tangents to a circle from a point are really the tangent segments.
B Tangent segments to a circle from a point are congruent .
7
To prove this corollary, prove ∆PAO ≅ ∆PBO by the HL Theorem.
Then PA = PB by CPCTC.
8
Theorem 9-2 If a line in the plane of a circle is perpendicular to the radius at its outer endpoint, then the line is tangent to the circle. Q l R
9
This is the converse of Theorem 9-1 and it also is proven with an indirect proof.
Q l R
10
example: RS is tangent to P at R. If PR = 5 and RS = 12, find PS.
11
CIRCUMSCRIBED POLYGON
… a polygon is circumscribed about a circle if each of its sides is tangent to the circle.
12
INSCRIBED CIRCLE … a circle is inscribed in a polygon
if each of the sides of the polygon is tangent to the circle.
13
CIRCUMSCRIBED POLYGON
and INSCRIBED CIRCLE are the same thing!
15
COMMON TANGENT … a line that is tangent to each
of two coplanar circles.
16
COMMON INTERNAL TANGENT
… intersects the segment joining the centers of the circles.
17
Here is another COMMON TANGENT.
18
COMMON EXTERNAL TANGENT
… does not intersect the segment joining the centers of the circles.
19
Are there anymore COMMON TANGENTS?
20
TANGENT CIRCLES … two coplanar circles that are tangent to the
same line at the same point. #1 Externally Tangent Circles
21
TANGENT CIRCLES … two coplanar circles that are tangent to the
same line at the same point. #2 Internally Tangent Circles
22
Classroom Exercises on page 335
Classroom Assignment Classroom Exercises on page 335 1 to 3 all numbers How can relationships in a circle allow you to solve problems involving segments, angles, and arcs?
23
Assignment Written Exercises on pages 335 to 337 RECOMMENDED: 1 to 7 odd numbers, 11 REQUIRED: 9, 16, 17, 18, 20, 21 How can relationships in a circle allow you to solve problems involving segments, angles, and arcs?
Similar presentations
