Question : In a circle, chords AB and CD intersect internally at E. If CD = 18 cm, DE = 5 cm, AE = 13 cm, then the length of BE is:
Option 1: 4 cm
Option 2: 7 cm
Option 3: 3 cm
Option 4: 5 cm
Correct Answer: 5 cm
Solution :
Given:
CD = 18 cm, DE = 5 cm, AE = 13 cm
Now,
CE = CD – DE = 18 – 5 = 13 cm
Let the length of BE be $x$.
According to the concept,
$\Rightarrow AE\ \times BE\ =\ CE\ \times DE$
$\Rightarrow 13\ \times x\ =\ 13\ \times 5$
$\Rightarrow x\ =\ 5$ cm
Hence, the correct answer is 5 cm.
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