Answer:
[tex]PT=15\ cm[/tex]
Step-by-step explanation:
we know that
PT is tangent at T to a circle whose center is O
That means----> Segment PT and segment OT are perpendicular lines
so
Triangle OPT is a right triangle
see the attached figure to better understand the problem
In the right triangle OPT of the figure
Applying the Pythagoras Theorem
[tex]OP^{2}=OT^{2}+PT^{2}[/tex]
we have
[tex]OP=17\ cm[/tex]
[tex]OT=8\ cm[/tex]
substitute and solve for PT
[tex]17^{2}=8^{2}+PT^{2}[/tex]
[tex]289=64+PT^{2}[/tex]
[tex]PT^{2}=289-64[/tex]
[tex]PT^{2}=225[/tex]
[tex]PT=15\ cm[/tex]
