Lecture 10.5 - Tangents

Lecture 10.5 - Tangents

G²

What do you call a dude that got too much sun?

Tangent

→​ a line in the same plane as a circle that intersects the circle in exactly one point.

That's not the tangent we're used to... or is it?​

What happens when that dude literally touches the sun?

Point of Tangency

→​ the point of intersection between circle and tangent

ouch!

What happens when the dude's buddy touches another planet and they have a line of sight?

Common Tangent

→​ line, ray, or segment that is tangent to two circles in the same plane

ouch!

Can you predict the relationship between point of tangency and center?

Figures > Words

​

Multiple Choice

What is this called?

• Tangent Line

• Secant

• Chord

• Diameter

Multiple Choice

A line that intersects the circle at one point.

• tangent

• secant

• chord

• diameter

Multiple Choice

How many common tangents?

• 0

• 1

• 2

• 3

• 4

Multiple Choice

How many common tangents?

• 0

• 1

• 2

• 3

• 4

Multiple Choice

How many common tangents?

• 0

• 1

• 2

• 3

• 4

Multiple Choice

How many common tangents?

• 0

• 1

• 2

• 3

• 4

RAISE THE PROOF

Can you imagine making a right triangle from this? Couldn't be me 😏

Multiple Choice

In the diagram, a tangent and a line drawn to the point of tangency form a right triangle. Solve for "?" (the length of the hypotenuse)

• 15

• 6

• -24

• 14

Multiple Choice

Find x.  Assume that segments that appear to be   tangent are tangent.

• 11.2
• 18.0
• 25.0
• 30.0

Multiple Choice

Solve for the missing side.

• 6.3

• 10.4

• 7.2

• 8.9

Multiple Choice

Find the radius r

• 2
• 3
• 4
• 5

RAISE THE PROOF

Again, can you imagine making a right triangle from this? Couldn't be me 😏

Multiple Choice

What is the value of x?

• 22
• 25
• 15
• 20

Multiple Choice

Find the length of BC.

• 2
• 3
• 9
• 14

Circumscribe yourself with people who make you happy

But really, can you imagine making a right triangle from this? Couldn't be me 😏

​When a polygon circumscribes a circle, the sides of the polygon become tangents. Each vertex of the polygon is called an external point where the tangents intersect. The distance from the external point to each point of tangency is the same.

Multiple Choice

Find the perimeter of the triangle.

• A
• B
• C
• D

Multiple Choice

If AB=8, AE=19, and CE=17, what is the measure of segment BC?

• 6 units

• 8 units

• 8.5 units

• 11 units

Multiple Choice

Assume that all the lines that appear tangent are tangent. Find the perimeter

• 54
• 36
• 48
• 42

Multiple Choice

Find the perimeter of the polygon.

• 77.8
• 73.4
• 78.8
• 67.4