Question

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

Answer 1

Answer:

Step-by-step explanation:

AC=12 units

Answer 2

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.

$OA^2=15^2+8^2$

$OA^2=225+64$

$OA^2=289$

$OA^2=17^2$

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.