Tangents to CirclesCircles

Secants and Tangents Secant

2 points of intersection

Tangent 1 point of intersection

Point of Tangency

Radii _|_ Chord What would you conclude about the

following diagram?

P

A

B

X

R

Radii _|_ Chord What would you conclude about the

following diagram?

P

A

B

X

R

AX XB ?

Prove it!

Radii & Tangent What would you conclude about the

following diagram?

P

A

Radii & Tangent Does this help??

P

A

Radii & Tangent The tangent is perpendicular to the

radius at the point of tangency

P

A

Inscribed Angles & Arcs An inscribed angle has its vertex ON

the circle.

Inscribed Angles & Arcs An inscribed angle has its vertex ON

the circle.In

terce

pte

d

arc

Inscribed Angles & Arcs What type of inscribed angle forms a

minor arc?M

inor

arc

Inscribed Angles & Arcs What type of inscribed angle forms a

major arc?M

ajo

r arc

Inscribed Angles & Arcs What type of inscribed angle forms a

semicircle?S

em

icircle

Inscribed Angle Theorem An angle inscribed in an arc has a

measure equal to ½ the measure of the intercepted arc.

60 120

Inscribed Angle Theorem What is the missing measure?

20

?

Inscribed Angle Theorem What is the missing measure?

90

?

Inscribed Angle Theorem What is the missing measure?

?

Inscribed Angle Theorem What is the missing measure?

40

?

Theorem If two inscribed angles intercept the

same arc, then they have the same measure

40

4080