Question

Medals for help.

Answer 1

okay

Answer 2

AB is tangent to circle O at A. The diagram is not drawn to scale.
if AO=21 and BC=14, what is AB?

Answer 3

what is your question?

Answer 4

I am back *Goes through the broken window* I am here to help

Answer 5

AO is the radius of circle O and is given to be 21. CO is also the radius of circle O, and because we were told what the radius is equal to (AO), we know that CO = AO = 21.
We are also given what BC is, so we know what BO is:
\[\overline{BO} = \overline{BC} + \overline{CO} = \overline{BC} + \overline{AO} = 14 + 21 = 35\]
AO is the radius of circle O. Because we're told that AB is tangent to circle O, we know that the angle that it forms (angle BAO) is a right angle (this is always true--a line tangent to a circle is always perpendicular to the radius).

Now we have a right triangle with the following measurements:
\[\overline{AO} = 21\]
\[\overline{BO} = 35\]
\[\overline{AB} = \ ?\]
What equation do you know of relates the sides of a right triangle? Using that, we can solve for side AB.