1. Intersections of Circles and Tangent Segments

2. S
𝑅𝑆 ≅ 𝑇𝑆
If two segments from the same exterior point are tangent to a circle, then they are congruent. R T
Party hat problems!

3. 1. Find the value of x.

4. 2. Find the value of x.

5. 3. Find the value of x.

6. 4. Find the value of x. B 3 A C 4 P D E

7. 5. Find the length of NP. N 4 4 T S 10 8 P R Q

8. More Pythagorean Theorem type problems! Yeah!! 
Point of Tangency
More Pythagorean Theorem type problems! Yeah!! 
If a line (segment or ray) is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency.

9. x = 15 92 + 122 = x2 leg2 + leg2 = hyp2 6. Find the value of x. A 12 B

10. RQ = 16 122 + (RQ)2 = 202 leg2 + leg2 = hyp2 7. Find the length of RQ.8 R Q
RQ = 16

11. 8. Is CB tangent to the circle?
leg2 + leg2 = hyp2? A 32
= 322 ? C 16 24 B No

12. r = 10 320 = 32r r2 + 242 = (r + 16)2 9. Find the radius.C
r = 10 24 B

13. 10. A green on a golf course is in the shape of a circle
10. A green on a golf course is in the shape of a circle. Your golf ball is 8 feet from the edge of the green and 32 feet from a point of tangency on the green.
What is the radius?
b) How far is your ball from the cup at the center?
x = 60 ft.
x = 68 ft.

14. Two circles can intersect:
in two points
one point
or no points

15. TWO points of intersection

16. One point of intersection are called Tangent Circles
Externally Tangent
Internally Tangent

17. No points of intersection, but different centers

18. Have no points of intersection, but the same center
Concentric Circles
Have no points of intersection, but the same center
Same center but different radii