If PT is a tangent at T to a circle whose centre is O and OP = 17 cm and OT = 8 cm, find the length of the tangent segment PT.
Answer & explanation
Correct answer: option 4
This, the length of the tangent TP is equal to:
\( {TP }^{2 } \) = \( {OP }^{2 } \) - \( {OT }^{2 } \)
\( {TP }^{2 } \) = \( {17 }^{2 } \) - \( {8 }^{2 } \)
\( {TP }^{2 } \) = 289 - 64
\( {TP }^{2 } \) = 225
TP = \(\sqrt { 225}\) = 15
Therefore, PT is 15 cm.