Date: Sec 10-1 Concept: Tangents to Circles Objective: Given a circle, identify parts and properties as measured by a s.g.
Mar 27, 2015
Date:
Sec 10-1
Concept: Tangents to Circles
Objective: Given a circle, identify parts and properties as measured by a s.g.
Circle Activity – Draw a diagram illustrating the words listed below. Identify each word on the illustration. LOOK IN CH 10
Circle
Center
Radius
Diameter
Chord
Secant
Tangent
Tangent Circles
Concentric
Common Tangent
Interior of a circle
Exterior of a circle
Point of Tangency
Minor Arc
Major Arc
Inscribed Angle
Central Angle
Example: The diagram shows the layout of the streets on Mexcaltitlan Island.
1. Name 2 secants
2. Name two chords
3. Is the diameter of the circle greater than HC?
4. If ΔLJK were drawn, one of its sides would be tangent to the circle. Which side is it?
Tangent Circles
2 points of intersection
1 point of intersection
No points of intersection
Draw internal/external tangents
Thm 10-1: If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency.
Pl
Q
QP l
If l is tangent to circle Q at P, then
Example: If BC is tangent to circle A, find the radius of the circle.
Use the pyth. Thm.
r2+242 = (r+16)2
r2+576 = (r+16)(r+16)
r2+576 = r2+16r+16r+256
r2+576 = r2+32r+256576 = 32r + 256
-256 -256
320 = 32r
32 32
10 = r
A16
24
rr
B C
Example: A green on a golf course is in the shape of a circle. A golf ball is 8 feet from the edge of the green and 28 feet from a point of tangency on the green, as shown at the right. Assume that the green is flat.
1. What is the radius of the green
2. How far is the golf ball from the cup at the center?
Thm 10-2: in a plane, if a line is perpendicular to a radius of a circle at its endpoint on the circle, then the line is tangent to the circle
Pl
Q If l QP at P, then l is tangent to circle Q
Example: Is CE tangent to circle D?
43
45D
EC
11
Use the Pyth. Thm:
112+432 = 452
121+1849 = 2025
1970 ≠ 2025
No, it’s not tangent
Thm: If 2 segments from the same exterior point are tangent to a circle, then they are congruent.
R
T
S
P
If SR and TS are tangent to circle P, then SR TS
Example: AB and DA are tangent to circle C. Find x.
X2 – 4 = 21
+ 4 +4
X2 = 25
X=5
B
D
C
AX2 - 4
21
Statements Reasons
1.
2. PQTQ; QSQR
3. PQ=TQ;
QS=QR
4. PQ+QS = TQ+QR
5.
6.
1.
2.
3.
4.
5. Seg. Addition Post.
6.
Today’s Work
In Class:
HW:
Center
Circle: A circle is the set of all points in a plane that are equidistant from a given point called the center of the circle. A circle with center P is called “circle P” or P
Radius
Diameter
Chord
Tangent
Secant