In Figure. O is the centre of a circle of radius 5 cm, T is a point such that OT = 13 cm and OT intersects the circle at E. If AB is the tangent to the circle at E, find the length of AB.
Answer
Solution
Given: Radius = 5 cm, OT = 13 cm
[ PT is tangent]
Using Pythagoras theorem OPT
PT and QT are tangents from same point
PT = QT = 12 cm
AT = PT – PA
AT = 12 – PA ..…(i)
Similarly BT = 12 – QB ..…(ii)
Since PA, PF and BF, BQ are tangents from point A and B respectively.
Hence, PA = AE ..…(iii)
BQ = BE ..…(iv)
AB is tangent at point E
Hence OE AB
ET = OT – OF
ET = 13 – 5
ET = 8 cm
In AET, using Pythagoras theorem
[using (i) and (ii)]
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