Question:
In the given figure, if AB = 8 cm and PE = 3 cm, then AE =
(a) 11 cm
(b) 7 cm
(c) 5 cm
(d) 3 cm
Solution:
We know that tangents drawn from the same external point will be equal in length.
Therefore,
AB = AC
It is given that,
AB = 8 cm
Hence,
AC = 8 cm …… (1)
Similarly,
PE = CE
It is given that,
PE = 3
Therefore,
CE = 3 …… (2)
Subtracting equations (1) and (2), we get,
AC − CE = 8 − 3
From the figure we can see that,
AC − CE = AE
Therefore,
AE = 8 − 3
AE = 5 cm
Option (c) is the correct answer.
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