MCQ
In the given figure, if $AB = 8\ cm$ and $PE = 3\ cm,$ then $AE =$
- A$11\ cm$
- B$7\ cm$
- ✓$5\ cm$
- D$3\ cm$
✓
Answer
Correct option: C.
$5\ cm$
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,
$PE = 3\ cm$
Therefore,
$CE = 3\ cm …… (2)$
Subtracting equations $(1)$ and $(2),$ we get,
$AC − CE = 8 − 3$
From the figure we can see that,
$AC − CE = AE$
Therefore,
$AE = 8 − 3$
$AE = 5\ cm$
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