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Tangents to Circles. Lengths of the lines. More Pythagorean Theorem type problems! Yeah!! . 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. 1. Find x. A. 12. B. 9. x. a 2 + b 2 = c 2.

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tangents to circles

Tangents to Circles

Lengths of the lines

slide2

More Pythagorean Theorem type problems! Yeah!! 

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.

slide3

1. Find x

A

12

B

9

x

a2 + b2 = c2

92 + 122 = x2

x = 15

slide4

2. Find RQ

a2 + b2 = c2

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

P

122 + (QR)2 = 202

12

8

RQ = 16

R

Q

slide5

r2 + 242 = (r + 16)2

3. Find the radius.

r2 + 576= r2 + 32r + 256

320= 32r

16

r = 10

A

C

24

B

slide6

S

Party hat problems!

If two segments from the same exterior point are tangent to a circle, then they are congruent.

R

T