Question

if PT is a tangent at T to a circle whose center is O and OP = 17 cm, OT =8 cm, Find the length of the tangent segment PT.

Answer 1

maybe your question is wrong OP must be 8cm and OT must be 13cm
so PT =√105

Answer 2

$\mathfrak{\red{Given}} \begin{cases} \sf{\orange{ OT = radius = 8 cm}} \\ \sf {\orange{OP = 17 cm}}\end{cases}$

To find: PT = length of tαngent =?

Cleαrly, T is point of contαct. And, we know thαt αt point of contαct tαngent αnd rαdius αre perpendiculαr.

∴ OTP is right αngled triαngle ∠OTP = 90°,

from Pythαgoras theorem OT² + PT² = OP²

8² + PT² = 17².

$\implies \sf 8^2 + PT^2=17^2$

$\implies \sf PT = \sqrt{172^2-8^2}$

$\implies \sf \sqrt{289-64}$

$\implies \sf \sqrt{225}$

∴ PT = length of tαngent = 15 cm.

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Hope it elps! :)