Question

AB is tangent to O. If AO = 32 and BC = 98, what is AB? my guess is 130? please help!

Answer 1

AO=CO
two congruent radii

Triangle ABO is a right-angled triangle

AO=32
BO=BC+CO=98+32=130
$AB=\sqrt{(121^2-32^2)}= \sqrt{15876} =126$

That is it!

Done :)

Use Pythagoras to calculate AB:

Answer 2

    
CO = AO  = 32    (Are rays.)
BO = BC + CO = 98 + 32 = 130
AB ⊥ BO
⇒  ΔAOB   is a rectangular triangle.
We use Pitagora's theorem.


$\displaystyle\\ AB = \sqrt{BO^2 - AO^2} = \sqrt{130^2 -32^2}=\\\\ = \sqrt{16900 -1024}= \sqrt{15876}= \boxed{126 }$