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.
[tex]OA^2=15^2+8^2[/tex]
[tex]OA^2=225+64[/tex]
[tex]OA^2=289[/tex]
[tex]OA^2=17^2[/tex]
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.
