Answer:
[tex]|AB|=30[/tex]
Step-by-step explanation:
From the diagram,
AO=OC=16 units, all radii of a circle are equal.
BO=OC+BC
BO=16+18
BO=34
A tangent to a circle will always meet the radius at right angles.
We use the Pythagoras Theorem to obtain:
[tex]|AB|^2+|AO|^2=|BO|^2[/tex]
[tex]|AB|^2+16^2=34^2[/tex]
[tex]|AB|^2+256=1156[/tex]
[tex]|AB|^2=1156-256[/tex]
[tex]|AB|^2=900[/tex]
Take positive square roots to get:
[tex]|AB|=\sqrt{900}[/tex]
[tex]|AB|=30[/tex]
