1. Date: Sec 10-1 Concept: Tangents to Circles
Objective: Given a circle, identify parts and properties as measured by a s.g.

2. Circle Center Radius Diameter Chord Secant Tangent Tangent Circles
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

3. 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?

4. Tangent Circles 2 points of intersection 1 point of intersection
Draw internal/external tangents
Tangent Circles
2 points of intersection
1 point of intersection
No points of intersection

5. QP  l P l If l is tangent to circle Q at P, then Q
Thm 10-1: If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency. P l Q
If l is tangent to circle Q at P, then
QP  l

6. 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+256 A 16 24 r B C
576 = 32r + 256
320 = 32r 32
10 = r

7. 1. What is the radius of the green
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?

8. If l  QP at P, then l is tangent to circle Q
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 P l Q
If l  QP at P, then l is tangent to circle Q

9. Example: Is CE tangent to circle D?43 45 D E C 11
Use the Pyth. Thm:
= 452
= 2025
1970 ≠ 2025
No, it’s not tangent

10. If SR and TS are tangent to circle P, then SR  TS
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

11. Example: AB and DA are tangent to circle C. Find x.21
X2 – 4 = 21
X2 = 25
X=5

12. Statements
Reasons 1. 2. 3. 4.
5. Seg. Addition Post. 6. 1.
2. PQTQ; QSQR
PQ=TQ;
QS=QR
4. PQ+QS = TQ+QR 5. 6.

13. Today’s Work
In Class:
HW:

14. 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
Tangent
Center
Radius
Diameter
Chord
Secant