AC is tangent to circle O at point C. What is the length of AB?

The length of AB is 9.

Solution:

Given data:

Radius OC = 8

Tangent AC = 15

The angle between the tangent and radius is always right angle.

∠C = 90°.

Hence OCA is a right triangle.

Using Pythagoras theorem,

In a right triangle square of the hypotenuse is equal to the sum of the squares of the other two sides.

Taking square root on both sides of the equation, we get

OA = 17

OB is the radius of the circle.

⇒ OB = 8

AB = OA – OB

     = 17 – 8

     = 9

AB = 9

Hence the length of AB is 9.

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional

c

step-by-step explanation: