honors geometry 9.2 march 1 - mhskarl.files.wordpress.com filet s ob & ot ab ab & bt bt ts t...
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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