Answer:
[tex]CT=11.08\ cm[/tex]
Step-by-step explanation:
step 1
Find the length BT in the right triangle ABT
Applying Pythagoras Theorem
[tex]BT^2=AB^2+AT^2[/tex]
substitute the given values
[tex]BT^2=5^2+12^2[/tex]
[tex]BT^2=169[/tex]
[tex]BT=13\ cm[/tex]
step 2
Find the length CT
Applying the Intersecting Secant-Tangent Theorem
we have that
[tex]AT^2=BT(CT)[/tex]
substitute the given values and solve for CT
[tex]12^2=13(CT)[/tex]
[tex]CT=144/13\\CT=11.08\ cm[/tex]
