Intersections of Circles and Tangent Segments S R

Intersections of Circles and Tangent Segments

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

1. Find the value of x.

2. Find the value of x.

3. Find the value of x.

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

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

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

6. Find the value of x. 2 leg + 2 leg = 2 hyp 2 9 + 2 12 = 2 x x = 15

7. Find the length of RQ. leg 2 + leg 2 = hyp 2 122 + (RQ)2 = (8+12)2 2 12 + 2 (RQ) = 2 20 RQ = 16

8. Is CB tangent to the circle? 2 leg + 2 leg = 2 16 + 2 hyp ? 2 24 = No 2 32 ?

9. Find the radius. 2 r + 2 24 = (r + 2 16) r 2 + 576 = r 2 + 32 r + 256 320 = 32 r r = 10

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. a) What is the radius? x = 60 ft. b) How far is your ball from the cup at the center? x = 68 ft.

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

TWO points of intersection

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

No points of intersection, but different centers

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