Hi everyone, Today's class was kind of confusing, so I'm

going to try to make it clear.

As usual we started the class by correcting the homework,

The problems that people had on the homework were

actually simple, it was just look carefully each inscribed angle

where is it and that the measurement of all arcs together is 360.

Today we learned:

Tangents

Point of tangency

Theorem 9-8, 9-9, and 9-10

Common Interior Tangent

Common Exterior Tangent

Circumscribed Polygons

( a lot, I know)

so...

Tangent

Definition: 

A line or a segment outside the circle

that intercepts exactly at only one point on the circle

(this point is the POINT OF TANGENCY)

Theorem 9-8:

If : You have a line tangent to a circle

     A Radius that goes to the point of tangency

Then : the radius is perpendicular to the tangent

Theorem 9-9 : Converse of 9-8

If : you have a radius;

     a line passing through only one point that is

     perpendicular to the radius

Then : The line is tangent

(same diagram from 9-8)

Theorem 9-10 

If : two segments that start from a point out of the circle,

     touching the point of tangency

Then : they are congruent

Common Interior Tangents

There are three different places that we can see

the INTERIOR(inside) part of the circle.

The EXTERIOR(outside) part of the circle.

And ON the circle.

If there are two circles

the space between them is also considered inside

The common Interior Tangent, is a tangent that passes

 through this inside part between two circles.

Common Exterior Tangent

Same as the interior, but in not in the interior part

Circumscribed Polygons 

Definition: Polygon whose sides are tangent to the circle

One interesting thing about Circumscribed polygons is that 

one Circumscribed polygons with infinite amount of sides

is a circle

The Homework is pg 479, # 17-40 except for 37

PS: This homework is really "versatil"