1. 30. Tangents to Circles

2. Tangents to Circles Std – MM2G3 – Understand properties of circles
EQ – What are the rules for tangents?

3. Vocabulary
A tangent is a line that intersects a circle at exactly one point.
The point at which a tangent intersects a circle is called the point of tangency.

4. Tangents between circles
Common internal tangent – a tangent of 2 circles that intersects the line connecting the centers
Common external tangent – a tangent of 2 circles that does not intersect the line connecting the centers

5. Name the segments

6. Fact #1
A line is tangent to a circle if and only if it is perpendicular to the radius drawn to the point of tangency.
radius
90 degrees = perpendicular
tangent

7. Example
Since a radius of the circle is 5, any radius is 5…
Since it is a radius drawn to a point of tangency, it is perpendicular to the tangent. 5
a2 + b2 = c2
= c2
= c2
169 = c2
13 = c ?
This whole length is 13.
x + 5 = 13
x = 8 5 12
ANSWER: x = 8

8. Example
Find KY

9. Fact #2
If two segments from the same exterior point are tangent to a circle, then they are congruent.
tangent #1
exterior point
tangent #2
They are congruent.

10. Example
exterior point
Because of Fact #2, x=14.

11. Example
Find x

12. Assignment
Pg. 186: #12-20 even

13. Assessment
Cube with partner