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.

hi there!

the answer will be d: 2