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(3) 20 / 3 cm
Step-by-step explanation:
Let O be the centre of the circle and let the chord PQ meet the line TO at R.
By symmetry, TO is the perpendicular bisector of PQ, so PR=4. Thus PRO is a right angled triangle with leg PR=4 and hypotenuse PO=5 (a radius). It follows that the other leg is RO=3.
Triangle TPO is also a right angle triangle, and its angle at O is the same as PRO's angle at O. So triangles TPO and PRO are similar.
Therefore
TP / PO = PR / RO
=> TP / 5 = 4 / 3
=> TP = 5 × 4 / 3 = 20 / 3
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