Download presentation

Presentation is loading. Please wait.

1
**Lines that intersect Circles**

Geometry H2 (Holt 12-1) K. Santos

2
Circle definition Circle: set of all points in a plane that are a given distance (radius) from a given point (center). Circle P P Radius: is a segment that connects the center of the circle to a point on the circle

3
**Interior & Exterior of a circle**

Interior of a circle: set of all the points inside the circle Exterior of a circle: set of all points outside the circle

4
**Lines & Segments that intersect a circle**

A G O B F E C D Chord: is a segment whose endpoints lie on a circle. Diameter: -a chord that contains the center -connects two points on the circle and passes through the center Secant: line that intersects a circle at two points

5
Tangent A tangent to a circle is a line in the plane of the circle that intersects the circle in exactly one point Tangent may be a line, ray, or segment The point where a circle and a tangent intersect is the point of tangency A B

6
Pairs of circles Congruent Circles: two circles that have congruent radii Concentric Circles: coplanar circles with the same center

7
Tangent Circles Tangent Circles: coplanar circles that intersect at exactly one point Internally tangent externally tangent circles circles

8
Common Tangent Common tangent: a line that is tangent to two circles Common external common internal tangents tangents

9
Theorem If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency. O A P B Given: 𝐴𝐵 is tangent to circle O Then: 𝐴𝐵 ⟘ 𝑂𝑃

10
Example 𝐸𝐷 is tangent to circle O. Radius is 5” and ED = 12” Find the length of 𝑂𝐷 . O E D

11
Example Find x. 130° x

12
Theorem If a line in the plane of a circle is perpendicular to a radius at its endpoint on the circle, then the line is tangent to the circle. O A P B Given: 𝐴𝐵 ⟘ 𝑂𝑃 Then: 𝐴𝐵 is tangent to circle O

13
**Example—Is there a tangent line?**

Determine if there is a tangent line?

14
Theorem If two segments are tangent to a circle from the same point, then the segments are congruent. A B C Given: 𝐴𝐵 and 𝐶𝐵 are tangents to the circle Then: 𝐴𝐵 ≅ 𝐶𝐵

15
Example: R 𝑅𝑇 and 𝑅𝑆 are tangent to circle Q. 2n – 1 n + 3 Find RS. T S

Similar presentations

OK

Exploring Circles. Definitions Notation: if the center is P then the circle can be denoted by סּP The points inside the circle form the circle's interior.

Exploring Circles. Definitions Notation: if the center is P then the circle can be denoted by סּP The points inside the circle form the circle's interior.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on sets for class 11th Ppt on field study example Ppt on conceptual art books Ppt on indian history in hindi Ppt on credit policy pdf Ppt on eddy current inspection Ppt on business environment nature concept and significance Ppt on nature and history of democracy in nepal s Ppt on area of parallelogram worksheet Ppt on urinary tract infection in children