CIRCLES: TANGENTS

TWO CIRCLES CAN INTERSECT…

in two points one point or no points

NO POINTS OF INTERSECTION (DIFFERENT CENTER)

NO POINTS OF INTERSECTION (SAME CENTER)

Same center but different radii

1 POINT OF INTERSECTION(TANGENT CIRCLES)

Internally Tangent

Externally Tangent

2 POINTS OF INTERSECTION

COMMON TANGENTS

Internal

COMMON TANGENTS

External

If a line (segment or ray) is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency.

Point of Tangenc

y

More Pythagorean Theorem type problems! Yeah!!

a2 + b2 = c2

x = 15

92 + 122 = x2

a2 + b2 = c2

RQ = 16

122 + (QR)2 = (8+12)2

122 + (QR)2 = 202

r2 + 242 = (r + 16)2

r = 10

r2 + 576 = r2 + 32r + 256320 = 32r

R

S

T

TSRS If two segments from

the same exterior point are tangent to a circle, then they are

congruent.

Party hat problems!

R

S

T

22 x

11 1122 x92 x

3 3 xorx

A

C

B152 x

x14

15x

AC

E

3

4

7X

B

D

X

P

TS

Q10 4

18NP

P

N

R

12