Honors Geometry_9.2_March 1

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Warmup

Refer to the diagram and identify:

a) two radii ______________

b) a secant ________

c) two chords _____________

d) a diameter _______

e) a tangent _______

f) a point of tangency _______

O

B

A

T S

OB & OT

ABAB & BT

BT

TST

Learning Target:

I can... identify tangents of a circle and apply theorems that relate tangents and radii. [G.C.A2]

9.2 Tangents

Theorem 9.1 If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency.

If line l is tangent to ⊙C at T,

then _______________

Theorem 9.2 If a line in the plane of a circle is perpendicular to a radius at its outer endpoint, then the line is tangent to the circle.

S

T

O

If ST ⟂ OT,

then ____________________________

CT ⟂ line l

ST is tangent to ⊙O

P

A

B

C

Corollary Tangents to a circle from a point are congruent.

Honors Geometry_9.2_March 1

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(opposite of 9.1 notes)

When each side of a polygon is tangent to a circle, the polygon is said to be CIRCUMSCRIBED ABOUT THE CIRCLE and the circle is INSCRIBED IN THE POLYGON.

Common Tangent: A line that is tangent to each of two coplanar circles.

* common INTERNAL tangent

- intersects the segment joining the centers

* common EXTERNAL tangent

- does not intersect the segment joining the centers.

Tangent Circles: are coplanar circles that are tangent to the same line at the same point

1. Is AB a tangent?

Practice Problems

2.

Honors Geometry_9.2_March 1

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R

T

X

O

a) if OR = 6 and OT = 8 then RT = ?

b) if m∠OTR = 45 and OT = 4, then RT = ?? and OR = ??

3. Given OT is tangent to circle R at point O...

c) if RO = 5, OT = 12

R

T

X

O

GivenOTistangenttocircleRatpointO...3. (cont)

find RX =

find XT =

find RT =

9.2 Assignment:

P. 335 CE #1-3; WE 1-6, 8, 10, 16, 20

Honors Geometry_9.2_March 1

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9.2 Assignment:

P. 335 CE #1-3; WE 1-6, 8, 10, 16, 20

Continued on next page

Continued on next page

Honors Geometry_9.2_March 1

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WE 1-6,8,10,16

1) 8 2) 2 34 3) 12 4) 15 5) 8.2 6) 12

8) 72,72; 18,18; 144; yes

10) OS SP; OP, OS; 12 12 5

16) 20, 18, 16

CE 1-3

1) 2, 2, 2, 2, 1, 0

2) 2, 1, 0, 0, 0, 0

3) b, e