Correct option is: (C) \(\frac{20}{3}cm\)
OR bisect chord PQ at right angle.
\(\therefore\) PR = QR = \(\frac {PQ}{2} = \frac 82\) = 4 cm & \(\angle\) PRO = 90°
In right \(\triangle\) PRO
\(OP^2 = OR^2 + PR^2\)
= \(OR^2 = OP^2 - PR^2 = 5^2-4^2\).
= 25-16 = 9
\(\therefore\) OR = 3 cm
Also triangles \(\triangle\) PRO& \(\triangle\) PRT are similar triangles.
as
\(\angle\) PRO = \(\angle\) PRT = 90°
\(\angle\) POR = \(\angle\) TPR
\(\angle\) OPR = \(\angle\) PTR
\(\therefore\) \(\frac {OP}{PT} = \frac {PR}{RT} = \frac {OR}{PR} \) (By property of similar triangles).
= \(\frac {OP}{PT} = \frac {OR}{PR} \)
= \(\frac {5}{PT} = \frac 34\)
= PT = \(\frac {5\times 4}3 = \frac {20}3 cm\)
